SSC CGL 202031)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:

Correct Option: A

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 202032)What is the smallest integer that is divisible by 3, 7 and 18?

Correct Option: B

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 202033)The largest number which should replace * in the number 2365*4 to make the number divisible by 4 is:

Correct Option: A

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 202034)If the number 687x29 is divisible by 9, then the value of 2x is:

Correct Option: B

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 202035)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:

Correct Option: C

-2

On changing the corresponding signs, \({(30\div5)-(84\div6)\times5\over[{2\over3}\times18]+(4\times2)}\) = -2

SSC CGL 202036)The greatest number which should replace '*’ in the number 146*48 to make it divisible by 8 is:

Correct Option: B

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 201637)

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

Correct Option: A

**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 202038)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)?

Correct Option: D

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 202039)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:

Correct Option: B

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 202040)If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of (x + y + z) ?

Correct Option: B

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.

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