# 1000+ TNPSC Aptitude Study Materials Pdf - 1

Question: 1

Twenty times a positive integer is less than its square by 96. What is the integer?

(A) 20

(B) 22

(C) 24

(D) 26

Ans: C

Let the integer be x.

Then, x2 - 20x = 96

⇔ x2 - 20x – 96 = 0

⇔ (x + 4) (x – 24) = 0

⇔ x = 24.

Question: 2

Two numbers are such that their difference, their sum and their product are to one another as 1 : 7 : 24. The product of the two numbers is

(A) 12

(B) 24

(C) 48

(D) 60

Ans: C

Let the numbers be x and y.

Let a - b = k ----(i)

a + b = 7k ------(ii)

ab = 24k

Adding (i) and (ii), we get : 2a = 8k or a = 4k.

Putting a = 4k in (i), we get : b = 3k.

Putting a = 4k and b = 3k in (iii), we get : 4k × 3k = 24 k ⇔ 122 = 24k ⇔ k = 2.

Hence, product of numbers = 24k = 24 × 2 = 48.

Question: 3

If the product of three consecutive integers is 120, then the sum of the integers is

(A) 9

(B) 12

(C) 15

(D) 18

Ans: C

120 = 2 × 2 × 2 × 3 × 5

= (2 × 2) × 5 × (2 × 3) = 4 × 5 × 6.

Clearly, the three consecutive integers whose product is 120 are 4, 5 and 6.

Required sum = 4 + 5 + 6 = 15.

Question: 4

Three numbers are in the ratio 3 : 2 : 5. The sum of their squares is 1862. Find the numbers.

(A) 3

(B) 7

(C) 9

(D) 10

Ans: B

Let the numbers be 3x, 2x and 5x.

Then, (3x)2 + (2x)2 + (5x)2 = 1862 ⇒ 9x2 + 4x2 + 25x2 = 1862

⇒ 382 = 1862 ⇒ x2 = \$\${1862}/ {38}\$\$ = 49 ⇒ x = \$\$√49\$\$ = 7

Hence, the numbers are 21, 14 and 35.

Question: 5

If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the numbers.

(A) 20

(B) 27

(C) 28

(D) 29

Ans: B

Then, x2 + (x + 2)2 + (x + 4)2 = 2531

⇒ 3x2 + 12x - 2511 = 0 ⇒ x2 + 4.

Hence, the required numbers are 27, 29 and 31.

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