SSC MTS 2017 PYQs

Question 1

Which smallest number must be subtracted from 400, so that the resulting number is completely divisible by 7?

Accepted Answer

Divide 400 by 7. The remainder is 1. To make 400 divisible by 7, subtract this remainder from 400. So, 400 - 1 = 399, which is divisible by 7.

Question 2

For what value of N, 23N7 is completely divisible by 9?

Accepted Answer

For a number to be divisible by 9, the sum of its digits must be divisible by 9. Here, 2+3+N+7 = 12+N. For 12+N to be divisible by 9, N must be 6 (12+6=18).

Question 3

How many times the digit 7 appears in the number from 1 to 90?

Accepted Answer

Count 7s in units place (7, 17, ..., 87) which are 9 times. Count 7s in tens place (70, 71, ..., 79) which are 10 times. Total = 9 + 10 = 19.

Question 4

Which smallest number must be added to 100, so that the resulting number is completely divisible by 6?

Accepted Answer

To be divisible by 6, a number must be divisible by both 2 and 3. 100 + 2 = 102. 102 is even (divisible by 2) and 1+0+2=3 (divisible by 3).

Question 5

What is the value of (2.3 + 1.7)2– (2.3 – 1.7)2?

Accepted Answer

Use the identity (a+b)² - (a-b)² = 4ab. Here a=2.3 and b=1.7. So, 4 * 2.3 * 1.7 = 4 * 3.91 = 15.64.

Question 6

What is the value of 34 ÷ 17 x 2 + 4?

Accepted Answer

Follow BODMAS/PEMDAS: first division (34 ÷ 17 = 2), then multiplication (2 x 2 = 4), and finally addition (4 + 4 = 8).

Question 7

If N = (√7 + √5) / (√7 - √5), then what is the simplified value of 1/N?

Accepted Answer

First, find 1/N by inverting N. Then, rationalize the denominator by multiplying the numerator and denominator by (√7 - √5). Simplify the expression to get the final answer.

Question 8

What is the value of (3.7)2- (1.7)2?

Accepted Answer

Use the identity a² - b² = (a - b)(a + b). Substitute a=3.7 and b=1.7 to get (3.7-1.7)(3.7+1.7) = (2)(5.4) = 10.8.

Question 9

What is the value of 38 ÷ 19 × 3 + 5?

Accepted Answer

Follow BODMAS/PEMDAS: first division (38 ÷ 19 = 2), then multiplication (2 × 3 = 6), and finally addition (6 + 5 = 11).

Question 10

The sum of three consecutive even integers is 84. Which is the least integer among them?

Accepted Answer

Let the integers be x, x+2, x+4. Their sum is 3x+6 = 84. So, 3x = 78, which means x = 26. The least integer is 26.

Question 11

Which of the following statement(s) is/are true?I. There are 13 multiples of 7 from 1 to 100.II. There are 5 multiples of 19 from 1 to 100.

Accepted Answer

To find multiples, divide the upper limit by the number. For 7, 100/7 = 14 with remainder. So there are 14 multiples. For 19, 100/19 = 5 with remainder. So there are 5 multiples. Statement II is true.

Question 12

What is the value of √(1500 + √441)?

Accepted Answer

First, calculate the square root of 441, which is 21. Then, add 21 to 1500 to get 1521. Finally, find the square root of 1521, which is 39.

Question 13

What is the value of 51 + 52 + 53 ……. 100?

Accepted Answer

The sum of an arithmetic series is (n/2)*(first term + last term). Here, n = 100 - 51 + 1 = 50. So, sum = (50/2)*(51 + 100) = 25 * 151 = 3775.

Question 14

What is the simplified value of 33/(6 - √3)?

Accepted Answer

To simplify, multiply the numerator and denominator by the conjugate of the denominator (6 + √3). This eliminates the square root from the denominator, resulting in (33 * (6 + √3)) / (36 - 3) = 33 * (6 + √3) / 33 = 6 + √3.

Question 15

What is the LCM of 18/5 and 20/9?

Accepted Answer

To find the LCM of fractions, calculate LCM of numerators (18, 20) and HCF of denominators (5, 9). LCM(18, 20) = 180, HCF(5, 9) = 1. So, LCM = 180/1 = 180.

Question 16

What is the unit digit of 1261 × 3474 × 1269 ?

Accepted Answer

To find the unit digit, multiply only the unit digits of each number: 1 × 4 × 9 = 36. The unit digit of 36 is 6.

Question 17

What is the value of 31+ 3-1+ 32+ 3-2?

Accepted Answer

Calculate each term: 3^1=3, 3^-1=1/3, 3^2=9, 3^-2=1/9. Sum them: 3 + 1/3 + 9 + 1/9 = 12 + 3/9 + 1/9 = 12 + 4/9 = 108/9 + 4/9 = 112/9.

Question 18

What is the Highest Common Factor of 3/4 and 12/13?

Accepted Answer

HCF of fractions is HCF of numerators divided by LCM of denominators. HCF(3, 12) = 3. LCM(4, 13) = 52. So, HCF = 3/52.

Question 19

A number exceeds its 1/6 by 30. What is the number?

Accepted Answer

Let the number be x. The equation is x - x/6 = 30. This simplifies to 5x/6 = 30, so x = 30 * 6 / 5 = 36.

Question 20

What is the value of 92+ 112+ …… 212?

Accepted Answer

The series is the sum of squares of consecutive odd numbers from 9 to 21. Calculate each square and add them: 81 + 121 + 169 + 225 + 289 + 361 + 441 = 1687.