objective Ques (194 results)
SSC CGL Mains 20241)The average of first 91 even numbers is
92
SSC CGL Mains 20242)
A)
B)
C)
D)
.
SSC CGL Mains 20243)Which number among 38211, 38121, 32118, and 31128 is divisible by 24?
31128
SSC CGL 20224)If a 7-digit number 54p3987 is divisible by 11, then p is equal to:
5
SSC CGL 20225)Find the HCF of 60, 148 and 382.
2
SSC CGL 20226)If the seven-digit number 52A6B7C is divisible by 33, and A, B, C are primes, then the maximum value of 2A + 3B + C is:
23
SSC CGL 20227)The HCF of three numbers 98, 175 and 210 will be:
7
SSC CGL 20228)Any six-digit number that is formed by repeating a three-digit number, is always divisible by:
1001
SSC CGL 20229)The LCM of 1.2 and 2.7 is:
10.8
SSC CGL 202210)The least number that should be added to 35460 so that the sum is exactly divisible by 3, 4, 5 and 7 is:
240
SSC CGL 202211)The HCF of two numbers is 21 and their LCM is 840. If one of the numbers is 147, then the other number is:
120
SSC CGL 202212)Determine the LCM of two numbers if their HCF is 9 and their ratio is 14 : 19.
2394
SSC CGL 202213)When m12 - 1 is divided by m + 1, the remainder is:
0
SSC CGL 202214)The HCF of two numbers is 17 and the other two factors of their LCM are 11 and 19. The smaller of the two numbers is:
187
SSC CGL 202215)Choose the option in which the numbers are in correct ascending order.
\({1 \over 11},{2 \over 9},{2 \over 3} and {4 \over 5}\)
SSC CGL 202216)If the number 6788934a4 is divisible by 11, then find the smallest whole number in the place of a.
2
SSC CGL 202217)The HCF of three numbers 72, 108 and 2010 is:
6
SSC CGL 202218)If the nine-digit number 3422213AB is divisible by 99, then what is the value of 2A + B?
11
SSC CGL 202219)If the 5-digit number 750PQ is divisible by 3, 7 and 11, then what is the value of P + 2Q?
17
SSC CGL 202220)What will be the remainder when 2727 + 27 is divided by 28?
26
SSC CGL 202221)Two numbers are in the ratio of 6 ∶ 5. If their HCF is 3, then what is the LCM of the two numbers?
90
SSC CGL 202222)What is the remainder when 8127 is divided by 8?
7
SSC CGL 202223)What is the ratio between the HCF and LCM of the numbers whose LCM is 48 and the product of the numbers is 384?
1 ∶ 6
SSC CGL 202224)The HCF of two numbers is 12. Which one of the following can never be their LCM?
90
SSC CGL 202225)If a nine-digit number 485x3678y is divisible by 72, then for the smallest value of x, the value of (2y - 3x) is:
8
SSC CGL 202226)LCM and HCF of two numbers are 90 and 15, respectively. If the sum of the two numbers is 75, then find the greater number.
45
SSC CGL 202227)If a 10-digit number 54726x79y6 is divisible by 72, then what is the value of 5x - 3y, for the least value of y?
16
SSC CGL 202228)Find the smallest number which should be added to the smallest number divisible by 6, 9 and 15 to make it a perfect square.
10
SSC CGL 202229)Find the sum of the greatest and the smallest number which may replace k in the number 3281k6 to make the number divisible by 6.
8
SSC CGL 202230)Which of the following is the smallest number that is a perfect square and is divisible by each of the numbers 6, 8 and 15?
3600
SSC CGL 202231)The least number which should be added to 3627 so that the sum is exactly divisible by 4, 5, 6 and 8 is:
93
SSC CGL 202232)If the number 48k2048p6 is divisible by 99, then (k × p) is equal to:
0
SSC CGL 202233)Find the value of k in the number 3426k if the number is divisible by 6 but NOT divisible by 5.
6
SSC CGL 202234)What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
900
SSC CGL 202235)Find the greatest 3-digit number which, when divided by 3, 4, 5 and 8, leaves remainder 2 in each case.
962
SSC CGL 202236)Find the value of k such that the number k53206k is divisible by 6.
4
SSC CGL 202237)If 8A5146B is divisible by 88, then what is the value of AB?
81
SSC CGL 202238)What is the LCM of 3.6, 1.8 and 0.144?
3.6
SSC CGL 202239)Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
69
SSC CGL 202240)If each of the two numbers 516 and 525 are divided by 6, the remainders are R1 and R2 respectively. What is the value of \(\frac{{{{\rm{R}}_{\rm{1}}}{\rm{ + }}{{\rm{R}}_{\rm{2}}}}}{{{{\rm{R}}_{\rm{2}}}}}\)?
6/5
SSC CGL 202241)A number 'n' when divided by 6 leaves remainder 2. What will be the remainder when (n2 + n + 2) is divided by 6?
2
SSC CGL 202242)The average of a set of 18 consecutive integers is 22.5. What is the largest integer in the set?
31
SSC CGL 202243)LCM of two number is 22 times their HCF. If one of the numbers is 132 and the sum of LCM and HCF is 276, then what is the other number?
24
SSC CGL 202244)If a nine digit number 468x5138y is divisible by 72, then the value of \( \sqrt {4x + 3y}\) is:
6
SSC CGL 202245)What is the greatest four-digit number which on being divided by 6, 7 and 8 leaves 4, 5 and 6 as remainders, respectively?
9910
SSC CGL 202246)The average of eight consecutive odd number is 28. The sum of the smallest and the largest number is:
56
SSC CGL 202247)The greatest number that divides 126, 224 and 608 leaving remainders 2, 7 and 19, respectively, is:
31
SSC CGL 202248)Find the greatest number 234a5b, which is divisible by 22, but NOT divisible by 5.
234652
SSC CGL 202249)If the nine-digit number 9m2365n48 is completely divisible by 88, what is the value of (m2 × n2), for the smallest value of n, where m and n are natural numbers?
64
SSC CGL 202250)What is the least number which when decreased by 7 is divisible by 15, 24, 28 and 32?
10087
SSC CGL 202251)If 8A5146B is divisible by 88, then what is the value of AB ?
12
SSC CGL 202252)A and B are two prime numbers such that A > B and their LCM is 209. The value of B2 – A is:
102
SSC CGL 202253)If the 9-digit number 7x79251y8 is divisible by 36, What is the value of (10x2 - 3y2) for the largest possible value of y?
298
SSC CGL 202254)13, a, b, c are four distinct numbers and the HCF of each pair of numbers (13, a); (13, b); (13, c) is 13, where a, b, c are each less than 60 and a < b < c. What is the value of \(\frac{{{\rm{a}}\,{\rm{ + }}\,{\rm{c}}}}{{\rm{b}}}\) ?
2
SSC CGL 202255)A and B are two prime numbers such that A > B and their LCM is 209. The value of A2 - B is:
350
SSC CGL 202256)The value of \( \frac{2}{7} - \frac{3}{8} -\) \( \left[ {2\frac{1}{4} \div 3\frac{1}{2}\,\,{\rm{of}}\,{\rm{1}}\frac{1}{3} + \left\{ {1\frac{{17}}{{40}}\, - \,\left( {3\, - \,1\frac{1}{5}\, - \,\frac{3}{8}} \right)} \right\}} \right] \)is:
\(- \frac{4}{7}\)
SSC CGL 202257)If 8A5146B is divisible by 88, then what is the value of BA?
64
SSC CGL 202258)If 8A5146B is divisible by 88, then what is the value of B - A?
1
SSC CGL 202259)Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
168
SSC CGL 202260)What is the remainder when the product of 335, 608 and 853 is divided by 13?
7
SSC CGL 202261)Which is the smallest multiple of 7, which leaves 5 as remainder in each case, when divided by 8, 9, 12 and 15?
1085
SSC CGL 202262)If the 7-digit number x8942y4 is divisible by 56, what is the value of (x2+ y) for the largest value of y, where x and y are natural numbers?
55
SSC CGL 202263)What is the greatest number by which when 156, 181 and 331 are divided, the remainder is 6 in each case?
25
SSC CGL 202264)How many numbers are there from 500 to 650 (including both) which are neither divisible by 3 nor by 7?
87
SSC CGL 202265)Find the greatest number which divides 108, 124 and 156, leaving the same remainder.
16
SSC CGL 202266)LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers is 240, then what is the other number?
210
SSC CGL 202267)Find the greatest number 23a68b, which is divisible by 3 but NOT divisible by 9.
239685
SSC CPO 202068)The HCF of two numbers is 29, and the other two factors of their LCM are 15 and 13. The smaller of the two numbers is:
377
SSC CPO 202069)When a number is successively divided by 3, 4 and 7, the remainder obtained is 2, 3 and 5, respectively. What will be the remainder when 42 divides the same number?
29
SSC CPO 202070)Five bells ring together at the intervals of 3, 5, 8, 9 and 10 seconds. All the bells ring simultaneously at the same time. They will again ring simultaneously after:
6 minutes
SSC CPO 202071)How many numbers between 300 and 700 are divisible by 5, 6 and 8?
3
SSC CPO 202072)What is the sum of the digits of the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11 ?
18
SSC CPO 202073)If 1433 × 1433 × 1422 × 1425 is divided by 10, what is the remainder ?
0
SSC CPO 202074)If a nine-digit number 785x3678y is divisible by 72, then the value of (x + y) is:
10
SSC CPO 202075)Two numbers are in the ratio 7 : 11. If their HCF is 28, then sum of the two numbers is:
504
SSC CPO 202076)How many numbers between 400 and 700 are divisible by 5, 6 and 7?
2
SSC CPO 202077)When a number is successively divided by 3, 4 and 7, the remainders obtained are 2, 3 and 5, respectively. What will be the remainder when 84 divides the same number?
71
SSC CPO 202078)What is the least number of soldiers that can be drawn up in troops of 10, 12, 15, 18 and 20 soldiers, and also in the form of a solid square?
900
SSC CPO 202079)The HCF of two numbers is 29, and the other two factors of their LCM are 15 and 13. The larger of the two number is:
435
SSC CPO 202080)The remainder when 72 × 73 × 78 × 76 is divided by 35 is:
8
SSC CPO 202081)The least number which is exactly divisible by 4, 5, 8, 10 and 12 is:
120
SSC CPO 202082)If six - digit number 5x2y6z is divisible by 7, 11 and 13, then the value of (x – y + 3z) is:
7
SSC CPO 202083)The remainder when 75× 73× 78× 76 is divided by 34 is:
12
SSC CPO 202084)The ratio of two numbers is 7 : 13 and their HCF is 8. Their LCM is:
728
SSC CPO 202085)The least number which is exactly divisible by 5, 6, 8, 10 and 12 is:
120
SSC CPO 202086)What is the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11?
1089
SSC CPO 202087)If 1433 × 1433 × 1422 × 1425 is divided by 12, then what is the remainder?
6
SSC CPO 202088)If a nine-digit number 785x3678y is divisible by 72, then the value of (x - y) is :
2
SSC CPO 202089)Sunita invested Rs. 12,000 on simple interest at the rate of 10% p.a. to obtain a total amount of Rs. 20,400 after a certain period. For how many years did she invest to obtain the above amount?
7
SSC CPO 202090)The value of \(\dfrac{40-\dfrac{3}{4} \ of \ 32}{37 - \dfrac{3}{4} \ of \ (34-6)} \) is :
1
SSC Selection Post Matric 202291)Find the sum of the greatest and smallest number which may replace k in the number 8130k36 so that the number is divisible by 8.
10
SSC Selection Post Matric 202292)If N = (307)38 + (524)20, then what is the unit digit of N?
5
SSC Selection Post Matric 202293)If the five-digit number 570xy is divisible by 231, then what is the value of (2x - y)?
3
SSC Selection Post Matric 202294)If a number N is divisible by 3, then which of the following is true?
(N + 12) is divisible by 3
SSC Selection Post Matric 202295)If the 9-digit number 9843x678y is divisible by 72, then what is the value of (x2 + y2 + xy)?
61
SSC Selection Post Matric 202296)When (218 - 1 ) is divided by 9, the remainder is:
0
SSC Selection Post Matric 202297)How many integers between 299 and 501 are divisible by 4 or 10?
61
SSC Selection Post Matric 202298)Which of the following is NOT divisible by 11?
7985314625
SSC Selection Post Matric 202299)When a number n is divided by 6, the reminder is 3. What will be the remainder when (n4 + n3 + n2 + 5n) is divided by 6?
0
SSC Selection Post Matric 2022100)If the nine-digit number 8698x138y is divisible by 72, then the value of \( \sqrt{3x + y}\) is:
5
SSC Selection Post Matric 2022101)If the 5-digit number 284xy is divisible by 3 and 77, then the value of (8x - y) is:
5
SSC Selection Post Matric 2022102)A 9-digit number 4856327xy is divisible by 9 and x - y = 6 what is the value of \(\sqrt {4x + 2y}\)?
6
SSC Selection Post Matric 2022103)Find the greatest 3 digit number divisible by 3, formed using the digits 0, 1, 2, 3, 5 without any repetition.
531
SSC Selection Post Matric 2022104)If a seven-digit number 7x634y2 is divisible by 88, then for the largest value of y, what is the difference of the values of x and y?
2
SSC Selection Post Matric 2022105)Find the value of \( { \sqrt{4p^3+14p+6} }\) such that a 6-digit number 602p0p is divisible by 9.
24
SSC Selection Post Matric 2022106)If the eight-digit number 9534x37y is divisible by 24, then what is the value of (3x + y), for the largest value of x ?
30
SSC Selection Post Matric 2022107)Find the number nearest to 51462, that is divisible by 8.
51464
SSC Selection Post Matric 2022108)If a 9-digit number 1039m837n is divisible by 72, then find the value of \(n^2-m\over4\).
7
SSC Selection Post Matric 2022109)Find the value of \(0.23^2-0.04^2\over0.09\).
0.57
SSC Selection Post Matric 2022110)If a nine-digit number 385x3678y is divisible by 72, then the value of (y—x) is:
3
SSC Selection Post Matric 2022111)Find the sum of the greatest 4-digit number divisible by 6 and the smallest 4-digit number divisible by 3.
10998
SSC CHSL 2021112)If the nine-digit number ‘8475639AB’ is divisible by 99, then what is the value of A and B?
A = 4, B = 8
SSC CHSL 2021113)If the nine-digit number 259876p05 is completely divisible by 11, then what is the value of (p2 + 5)?
54
SSC CHSL 2021114)If the five-digit number 457ab is divisible by 3, 7 and 11, then what is the value of a2 + b2 - ab?
49
SSC CHSL 2021115)The largest six-digit number exactly divisible by 243 is:
999945
SSC CHSL 2021116)The smallest six-digit number that is exactly divisible by 53 is:
100011
SSC CHSL 2021117)When a number is divided by 3, the remainder is 2. Again, when the quotient is divided by 7, the remainder is 5. What will be the remainder when the original number is divided by 21?
17
SSC CHSL 2021118)A man covers \(5\over12\) of a total journey by train, \(\frac{7}{18}\) of the journey by bus and the remaining 7 km on foot. His total journey (in km) is:
36 km
SSC CHSL 2021119)If the 11-digit number 4y6884805x6 is divisible by 72, and x ≠ y, then the value of √xy is:
√6
SSC CHSL 2021120)If the number 4A306768B2 is divisible by both 8 and 11, then the smallest possible values of A and B will be:
A = 5, B = 3
SSC CHSL 2021121)What is the sum of all the possible values of k for which a seven-digit number 23k567k is divisible by 3?
15
SSC CHSL 2021122)If 3147 + 4347 is divided by 37, the remainder is:
0
SSC CHSL 2021123)The value of
28 ÷ [25 + 8 ÷ 4 - {25 + (25 of 8 ÷ 20) - (125 ÷ 5 of 25)}] + (25 × 5) is:
121
SSC CHSL 2021124)If the number 645A2879B8 is divisible by both 8 and 9, then the smallest possible values of A and B will be:
A = 3, B = 2
SSC CHSL 2021125)If (40√5x3 - 2√2y3) ÷ (2√5x - √2y) = Ax2 + By2 - Cxy, then find the value of A + 3B - √10C.
46
SSC CHSL 2021126)If 7183 + 7383 is divisible by 36, the remainder is:
0
SSC CHSL 2021127)When a positive integer 'n’ is divided by 12, the remainder is 5. What will be the remainder if 8n2 + 7 is divided by 12?
3
SSC CHSL 2021128)If the nine-digit number 87605x31y is divisible by 72, then the value of 2x-3y is:
2
SSC CHSL 2021129)If the number 34k56k is divisible by 6, then what will be the largest value of k?
6
SSC CHSL 2021130)If the number 87m6203m is divisible by 6, then find the sum of all possible values of 'm'
10
SSC CHSL 2021131)If a nine-digit number 489x6378y is divisible by 72, then the value of \(\sqrt{8x+6y}\) will be:
8
SSC CHSL 2021132)If the five-digit number 672 xy is divisible by 3, 7 and 11, then what is the value of (6x + 5y)?
17
SSC CHSL 2021133)When (224 – 1) is divided by 7, the remainder is:
0
SSC CHSL 2021134)If a number 54k31m82 is divisible by 11, what will be the maximum value of (k + m) ?
13
SSC CHSL 2021135)What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21 and 5?
99120
SSC CHSL 2021136)When a number M is divided by 7, the remainder is 6. What is the remainder if the square of M is divided by 7?
1
SSC CHSL 2021137)The difference between a number and its three-fifth is 274. What is 20% of the number?
137
SSC CHSL 2021138)If the nine-digit number 48x4923y8 is divisible by 88, then the value of (6x + 5y) for the maximum value of y, will be:
72
SSC CHSL 2021139)The six-digit number 537xy5 is divisible by 125. How many such six-digit numbers are there?
4
SSC CHSL 2021140)If an eleven-digit number 6578x43267y is divisible by 72, then the value of \(\sqrt{x+6y}\) will be:
4
SSC CHSL 2021141)Which of the following is divisible by 88?
2776400
SSC CHSL 2021142)n = 475AB is a positive integer whose tens and units digits are A and B, respectively. If n is divisible by 5, 8 and 9, then what is (10A + B) ?
20
SSC CHSL 2021143)If the number 579683pq is divisible by both 5 and 8, then the smallest possible values of p and q will be:
P = 2,q = 0
SSC CHSL 2021144)Three numbers are in the ratio \({3\over4}:{5\over8}:{7\over12}\). If the difference between the greatest and the smallest number is 48, then the value of the greatest number will be:
216
SSC CHSL 2021145)When an integer n is divided by 6, the remainder is 5. What is the remainder if 9n is divided by 6?
3
SSC CHSL 2021146)If the nine-digit number 23541y49x is divisible by 72, then (3x + 5y) ∶ (5x + 3y) is equal to:
7 ∶ 9
SSC CHSL 2021147)If the number 583p2310q2 is divisible by 11, then what is the value of p × q. where p > q?
0
SSC CHSL 2021148)If a number is divisible by 624, the remainder will be 53, If the same number is divisible by 16, then the remainder will be:
5
SSC CHSL 2021149)What is the least 6-digit number that is divisible 71?
100039
SSC CHSL 2021150)If a nine-digit number 1263487xy is divisible by both 8 and 5, then the greatest possible values of x and y, respectively, are:
6 and 0
SSC CHSL 2021151)The sum of two numbers is 59 and their product is 1150. Find the sum of their squares.
1178
SSC CHSL 2021152)If the difference between two numbers is 5 and the difference between their cubes is 1850, then the difference between their squares is:
5√485
SSC CHSL 2021153)If the number A9257B684 is divisible by 11, then what is the least value of A - B?
-8
SSC CHSL 2021154)What is the product of the largest and the smallest possible values of m for which a number 5m83m4m1 is divisible by 9 ?
16
SSC CGL 2020155)If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of (x + y + z) ?
16
To be divisible by 99, the number has to be divisible by 11 and 9 both.
For divisibility by 11,
7 + 8 + 6 + 8 + 9 - 0 + x + y + z
(38 - x + y + z) has to be divisible by 11.
For divisibility by 9,
(38 + x + y + z) has to be divisible by 9.
By option C),
x + y + z = 16
(38 - x + y + z) = 38 - 16 = 22 is divisible by 11.
(38 + x + y + z) = 38 + 16 = 54 is divisible by 9.
SSC CGL 2020156)When a positive integer is divided by d, the remainder is 15. When ten times of the same number is divided by d. the remainder is 6. The least possible value of d is:
16
Dividing by d, remainder = 15; \(\therefore d >15\) ;
from options, Let d = 16
\(\therefore\) Positive integer = 31;
Again, dividing 310 by 16, remainder = 6 ;
\(\therefore\) Minimum possible value of d = 16
SSC CGL 2020157)A certain value of x is added to each of 10, 16, 22 and 32, such that the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?
15
If x is added to each of numbers, the numbers so obtained in this order are in proportion
so,\( \frac{10 + x}{16 + x} = \frac{22 + x}{32 + x}\);
(10 + x)(32 + x) = (16 + x)(22 + x);
\(320 + 10x + 32x + x^2 = 352 + 16x + 22x + x^2\);
320 + 42x = 352 + 38x;
x = 8;
(x + 1) = 8 + 1 = 9;
(3x + 1) = 24 + 1 = 25;
Mean proportional =\( \sqrt{9 \times 25} = 15\)
SSC CGL 2016158)When a number is divided by 56, the remainder will be 29. If the same number is divided by 8, then the remainder will be
When a number is divided by 56, the remainder will be 29. If the same number is divided by 8, then the remainder will be
SSC CGL 2020159)The greatest number which should replace '*’ in the number 146*48 to make it divisible by 8 is:
8
146*48 is divisible by 8.
For divisibility by 8, number *48 must be divisible by 8
It is true for * = 2, 4, 6 and 8.
\(\therefore\) Maximum value of * = 8
SSC CGL 2020160)If ‘+’ means ‘-’, ‘-’ means ‘+’, ‘\(\times\)’ means ‘\(\div\) ’ and ‘\(\div\) ’ means ‘\(\times\)’, then the value of \({(30\times5)+(84\times6)\div5\over[{2\over3}\div18]-(4\div2)}\) is:
-2
On changing the corresponding signs, \({(30\div5)-(84\div6)\times5\over[{2\over3}\times18]+(4\times2)}\) = -2
SSC CGL 2020161)If the number 687x29 is divisible by 9, then the value of 2x is:
8
Divisibility rule by 9, if the sum of all number is divisible by 9 then number is divisible by 9.
Sum of number = 6 + 8 + 7 + x + 2 + 9 = 32 + x;
putting the value of x = 4;
32 + 4 = 36 divisible by 9 so,
2x = 2 x 4 = 8
SSC CGL 2020162)The largest number which should replace * in the number 2365*4 to make the number divisible by 4 is:
8
2365*4 is divisible by 4. For divisibility by 4, *4 should be divisible by 4. Possible value of * = 2, 4, 6, 8 Maximum value of * = 8
SSC CGL 2020163)What is the smallest integer that is divisible by 3, 7 and 18?
126
LCM of of 3, 7 and 18 = 126;
\(\therefore\)126 is the smallest integer that is divisible by 3, 7 and 18.
SSC CGL 2020164)The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4. The difference between greatest number and smallest number is:
21
Let the smallest number be x.
Numbers are x, 2x, 4x.
The sum of the squares of 3 natural numbers = 1029;
\(x^2 + (2x)^2 + (4x)^2 = 1029\);
\(x^2 + 4x^2 + 16x^2 = 1029\);
\(x^2 = 1029/21\);
\(x^2 = 49\);
x = 7;
Smallest number = 7;
Greatest number = 4x = 4 \times 7 = 28;
The difference between greatest number and smallest number = 28 - 7 = 21
SSC CGL 2020165)If the given number 925x85 is divisible by 11, then the smallest value of x is:
4
925x85 is divisible by 11. Then, Sum of digits at even places - sum of digits at odd places = 11. ⇒(9 + 5 + 8)-(2 + x + 5) = 11;⇒ x = 4
SSC CGL 2020166)If a positive integer n is divided by 7 the remainder is 2. Which of the following numbers gives a remainder of 0 when divided by 7?
n + 5
Dividing n by 7, remainder = 2; n + (7 - 2) = n + 5 is exactly divisible by 7.
Look: \(16\div7\), Remainder = 2; \(21\div7\), Remainder = 0
SSC CGL 2020167)What is the remainder when we divide \(5^{70}+7^{70}\) by 74 ?
0
\(5^{70}+7^{70}={(5^2)}^{35}+{(7^2)}^{35}=(25)^{35}+(49)^{35}\); When n is odd then \((x^n+a^n)\) is divisible by (x + a). Here, n = 35 (odd). So \((25)^{35}+(49)^{35}\) is divisible by (25 + 49) = 74;
Remainder = 0
SSC CGL 2020168)The greatest digit which may replace * in the number 1190*6 to make the number divisible by 9 is :
1
1190*6, is divisble by p. so 1+1+9+0+*+6=(17+*) is a multiple of 9. ⇒17+* =18; ⇒ *= 18 - 17 = 1
SSC CGL 2020169)If integer n is divided by 5, the remainder is 2. What will be the remainder if 7n is divided by 5?
4
Let n = 5k + 2 where k = quotient; 7n = 7(5k + 2) = 35k + 14 = \(5\times7k+10+4\) = 5(7k + 2) + 4; so remainder = 4
SSC CGL 2020170)When 2 is subtracted from each of the given n numbers, then the sum of the numbers so obtained is 102. When 5 is subtracted from each of them, then the sum of the numbers so obtained is 12. What is the average of the given n numbers?
5.4
Let for 'n' numbers the average be 'x'.
So, the total sum of 'n' numbers would be 'nx'.
If 2 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = 2n;
Thus, value of the total sum now = (nx - 2n);
Given that, this value equals to 102.
So, nx - 2n = 102 ...(1);
Again when 5 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = 5n;
Thus, value of the total sum now = (nx - 5n);
Given that, this value equals to 12.
So, nx - 5n = 12 ...(2);
Subtracting (2) from (1), we get:
nx - 2n - (nx - 5n) = 102 - 12; ⇒ -2n + 5n = 90; ⇒ 3n = 90 ;⇒ n = 90/3 = 30;
There are 30 numbers.
Putting n = 30, in eqn.(1), we get:
(30)x - 2(30) = 102; ⇒ 30x - 60 = 102; ⇒ 30x = 162; ⇒ x = 162/30 = 5.4
SSC CGL 2019171)If \(\sqrt{10-2\sqrt{21}}\)\(+\sqrt{8+2\sqrt{15}}\)\(=\sqrt a+\sqrt b\), where a and b are positive integers, then the value of \(\sqrt{ab}\) is closest to :
5.9
\(\sqrt{10-2\sqrt{21}}=\sqrt{(\sqrt{7})^2+(\sqrt3)^2-2\sqrt{7}\times \sqrt{3}}=\sqrt{(\sqrt{7}-\sqrt{3})^2}\)
Similarly
\(\sqrt{8+2\sqrt{15}}=\sqrt{(\sqrt{5})^2+(\sqrt3)^2+2\sqrt{5}\times \sqrt{3}}=\sqrt{(\sqrt{5}+\sqrt{3})^2}\)
therefore
\(\sqrt a+\sqrt b = \sqrt 5+\sqrt 7\);
a= 5; b=7
there approx value of \({\sqrt{35}} \) = 5.9 (approx)
SSC CGL 2019172)When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is:
8
SSC CGL 2019173)Let x be the least number which when divided by 15, 18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?
39
SSC CGL 2019174)If \(x=(164)^{169}+(333)^{337}\)\(-(727)^{726}\), then what is the unit's digit of x ?
8
SSC CGL 2019175)The number of factors of 3600 is :
45
SSC CGL 2019176)The HCF of two numbers is 21 and their LCM is 221 times the HCF. If one of the numbers lies between 200 and 300, then the sum of the digits of the other number is:
15
SSC CGL 2019177)If the 11-digit number 5678x43267y is divisible by 72, then the value of \(\sqrt{5x+8y}\) is:
6
SSC CGL 2019178)Three fractions, x, y and z, are such that x>y>z. When the smallest of them is divided by the greatest, the result is \(9\over16\) , which exceeds y by 0.0625.If \(x+y+z=1\frac{13}{24}\), then the value of (x + y) is
\(25\over24\)
SSC CGL 2019179)Two-third of the number of employees of a company are males and the rest are females. If \(3\over8\) of the male employees and \(2\over5\) of the female employees are temporary employees and the total number of permanent employees is 740, then \(7\over15\) of the total number of employees exceeds the number of female employees by:
400
SSC CGL 2019180)In an office \(5\over8\), of the total number of employees are males and the rest are females. \(2\over5\) of the number of males are non technical workers while \(2\over3\) of the number of females are technical workers, What fraction of the total number of employees are technical workers?
\(5\over8\)
SSC CGL 2019181)Two positive numbers differ by 2001, When the larger number is divided by the smaller number, the quotient is 9 and the remainder is 41. The sum of the digits of the larger number is:
14
SSC CGL 2019182)What is the remainder when \((127^{97}+97^{97})\) is divided by 32?
0
SSC CGL 2019183)If a 10-digit number 5 4 3 2 y 1 7 4 9 x is divisible by 72, then what is the value of (5x - 4y)?
14
SSC CGL 2019184)In finding the HCF of two numbers by division method, the last divisor is 17 and the quotients are 1. 11 and 2, respectively. What is sum of the two numbers?
816
SSC CGL 2019185)The LCM of two numbers x and y is 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x + y = ?
348
SSC CGL 2019186)If x is the remainder when \(3^{61284}\) is divided by 5 and y is the remainder when \(4^{96}\) is divided by 6, then what is the value of \((2x-y)\) ?
-2
x is the remainder when \(3^{61284}\) is divided by 5; So, \({3^{61284}\over5}={3^{4\times15321}\over5}\) ; \({3^4\over5}={81\over5}\); Remainder = 1; x=1;
y is the remainder when \(4^{96}\) is divided by 6; remainder is always '4'; thereforey = 4.
2x-y = 2-4 = -2
SSC CGL 2019187)The sum of the digits of a two-digit number is \( \frac{1}{7} \) of the number. The units digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7, the remainder will be:
6
Let the number be (10a + b).
ATQ,
a + b =\( \frac{10a + b}{7}\);
7a + 7b = 10a + b;
6b = 3a;
2b = a ---(1);
a - b = 4 ---(2);
From eq (1) and (2),
2b - b = 4;
b = 4;
a = \(4 \times 2
\)= 8;
Number = 10a + b = \(10 \times 8 + 4 =\) 84;
reverse of the number = 48;
Remainder after divide by 7 = 48/7 = 6
SSC CGL 2019188)Let \(x= (633)^{24} - \)\((277)^{38} + (266)^{54}\). What is the units digit of x ?
8
x = \((633)^{24} - (277)^{38} + (266)^{54}\)For the unit digit,
24 = 4 \times 6 + 0(remainder);
38 = 4 \times 9 + 2(remainder);
54 = 4 \times 13 + 2(remainder);
Now,
(Base number unit digit)^{remainder}
= \((3)^0 - (7)^2 + (6)^2\);
On consider unit digit,
= 1 - 9 + 6 = 7 - 9;
or 17 - 9 = 8;
8 is the units digit of x.
SSC CGL 2019189)One of the factors of\( (8^{2k} + 5^{2k})\), where k is an odd number, is:
89
\((8^{2k} + 5^{2k})\),k is odd nuber so,
Let the k be 1.
=\((8^{2} + 5^{2})\)
= 64 + 25 = 89
SSC CGL 2019190)When 7897, 8110 and 8536 are divided by the greatest number x, then the remainder in each case is the same. The sum of the digits of x is:
6
Let the remainder be k. 7897 - k = ax ; 8110 - k = bx; 8536 - k = cx ; Common factor is x. So difference between the numbers, 8110 - 7897 = 213 ; 8536 - 8110 = 426; 8536 - 7897 = 639 ; HCF of 213, 426 and 639 is 213. x = 213; Sum of the digits of x = 2 + 1 + 3 = 6
SSC CGL 2019191)When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 but x is divisible by 7. What is the digit at the thousand's place in x ?
8
Number = (LCM of 12, 16, 18, 20 and 25)k + 4
= 3600k + 4;
The number should be divisible by the 7 so,
Value of K = 5;
Number = \(3600 \times 5 + 4 \)= 18000 + 4 = 18004;
The digit at the thousands’ place = 8
SSC CGL 2019192)If a nine-digit number 389x 6378y is divisible by 72, then the value of \(\sqrt{6x+7y}\) will be :
8
389x6378y is divisible by 72,
Factor of 72 = \(8 \times 9;\)
So, number is divisible by 8 and 9 both.
Divisibility rule for 8,
78y (last three digits should be divisible by 8);
784 is divisible by 8 so,
Value of y = 4;
Divisibility rule of 9,
3 + 8 + 9 + x + 6 + 3 + 7+ 8 + 4
= 48 + x;
54 is divisible by 9;
So, x = 54 - 48 = 6;
Value of\( \sqrt{6x + 7y} = \sqrt{6 \times 6 + 7 \times 4} = \sqrt{36 + 28} =\sqrt{64} = 8\)
SSC CGL 2019193)Let a, b and c be the fractions such that a < b < c. If c is divided by a, the result is \({5\over2}\), which exceeds b by \({7\over4}\).
If a + b + c = 1\({11 \over 12}\), then (c - a) will be equal to :
\({1 \over 2}\)
ATQ,
\(\frac{c}{a} = \frac{5}{2};\)
c = \(\frac{5a}{2};\)
b = \(\frac{5}{2} - \frac{7}{4} = \frac{3}{4};\)
a + b + c = \(1\frac{11}{12} = \frac{23}{12};\)
a +\( \frac{3}{4} + \frac{5a}{2} = \frac{23}{12};\)
\(\frac{7a}{2} = \frac{23}{12} - \frac{3}{4};\)
7a = \( \frac{23}{6} - \frac{3}{2};\)
7a = \( \frac{7}{3} \);
a = \( \frac{1}{3} \);
c =\( \frac{5}{2} \times \frac{1}{3} = \frac{5}{6};\)
c - a =\( \frac{5}{6} - \frac{1}{3} = \frac{1}{2}\)
SSC CGL 2020194)What is the smallest interger that is a multiple of 5, 8 and 15 ?
120
LCM of 5, 8, 15 is 120