1000+ CTS Aptitude Questions and Answers Pdf - 1

Question: 1

The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is

(A) 20

(B) 22

(D) 169

View Answer

Ans: C

Let the numbers be x and y.

Then, xy = 120 and x² + y² = 289.

∴ (x + y)² = x² + y² + 2xy = 289 + 240 = 529.

∴ x + y = $$√529$$ = 23.

Question: 2

The sum of four consecutive even integers is 1284. The greatest of them is

(A) 318

(B) 320

(D) 324

View Answer

Ans: D

Let the four integers be x, x + 2, x + 4 and x + 6.

Then, x + (x + 2) + (x + 4) + (x + 6) = 1284

⇔ 4x = 1272

⇔ x = 318.

∴ Greatest integer = x + 6 = 324.

Question: 3

The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

(A) 3

(B) 4

(D) 9

View Answer

Ans: B

Let the ten’s digit be x and unit’s digit be y.

Then, (10x + y) - (10y + x) = 36

⇔ 9(x - y) = 36

⇔ x - y = 4.

Question: 4

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

(A) 10

(B) 20

(D) 50

View Answer

Ans: B

Let the number be a, b and c.

Then, a² + b² + c² = 138 and (ab + bc+ ca) = 131.

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

= 138 + 2 × 131 = 400

⇒ (a + b + c) = $$√400$$ = 20.

Question: 5

The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?

(A) 4

(B) 8

(D) 16

View Answer

An: B

Since the number is greater than the number obtained on reversing the digits, so the ten’s digit is greater than the unit’s digit.

Let the ten’s and unit’s digits be 2x and x respectively.

Then, (10 × 2x + x) – (10x + 2x) = 36

⇔ 9x = 36 ⇔ x = 4.

∴ Required difference = (2x + x) - (2x - x) = 2x = 8.

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1000+ CTS Aptitude Questions and Answers Pdf - 1

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