SSC CGL 20201)What is the smallest interger that is a multiple of 5, 8 and 15 ?

Correct Option: D

120

LCM of 5, 8, 15 is 120

SSC CGL 20192)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 :

Correct Option: D

\({1 \over 2}\)

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 20193)If a nine-digit number 389x 6378y is divisible by 72, then the value of \(\sqrt{6x+7y}\) will be :

Correct Option: D

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 20194)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 ?

Correct Option: B

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 20195)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:

Correct Option: D

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 20196)One of the factors of\( (8^{2k} + 5^{2k})\), where k is an odd number, is:

Correct Option: D

89

\((8^{2k} + 5^{2k})\),k is odd nuber so,

Let the k be 1.

=\((8^{2} + 5^{2})\)

= 64 + 25 = 89

SSC CGL 20197)Let \(x= (633)^{24} - \)\((277)^{38} + (266)^{54}\). What is the units digit of x ?

Correct Option: D

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 20198)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:

Correct Option: D

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 20199)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 \((2x-y)\) ?

Correct Option: C

-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 201910)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 = ?

Correct Option: D

348

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