GATE Questions and Answers with Explanation

Q:

217 x 217 + 183 x 183 = ?

A) 84521	B) 87487
C) 80578	D) 78458

Answer & Explanation Answer: C) 80578

Explanation:

${(217)}^{2} + {(183)}^{2}$

= ${(200 + 17)}^{2} + {(200 - 17)}^{2}$

It is in the form of ${(a + b)}^{2} + {(a - b)}^{2} = 2 (a^{2} + b^{2})$

= 2(40000 + 289) = 80578.

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Q:

What will come in place of question mark (?) in the following question?

$\frac{3}{4} of \frac{3}{5} of \frac{2}{3} of ? = 3174$

A) 10550	B) 10540
C) 10580	D) 10500

Answer & Explanation Answer: C) 10580

Explanation:

$\frac{2}{3} x \frac{3}{5} x \frac{3}{4} x ? = 3174 3174 x 10 / 3 = 10580$

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Filed Under: Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams , GATE

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Q:

There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number ?

A) 17	B) 19
C) 13	D) 11

Answer & Explanation Answer: C) 13

Explanation:

(385/1001) = 5/13

First Number is 5

=> Fourth number is 13

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Filed Under: Problems on Numbers
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Q:

If 'A$B' means ' A is father of B ', 'A#B' means ' A is daughter of B ', 'A@B' means ' A is sister of B ' then how is K related to Lin "H@K$L#M" ?

A) Husband	B) Uncle
C) Father	D) Cannot be determined

Answer & Explanation Answer: A) Husband

Explanation:

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Q:

Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ?

A) 3 : 4	B) 4 : 3
C) 2 : 3	D) 3 : 2

Answer & Explanation Answer: B) 4 : 3

Explanation:

Let us name the trains as A and B.

Then, (A's speed) : (B's speed)

= √b : √a = √16 : √9 = 4:3

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Q:

Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?

A) 12,421	B) 9,423
C) 11,600	D) 10,500

Answer & Explanation Answer: D) 10,500

Explanation:

The ratio of their investments:
50000x36 : 80000x30 = 3 : 4
Simran's share of profit = (24500x3/7) = Rs.10,500.

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Filed Under: Partnership
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Q:

A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

A) 90 mts	B) 150 mts
C) 120 mts	D) 100 mts

Answer & Explanation Answer: D) 100 mts

Explanation:

We know that $S p e e d = \frac{d i s \tan c e}{t i m e}$

distance= speed * time

$\Rightarrow$ $d = (40 \times \frac{5}{18}) \times 9$

d= 100 mts.

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Filed Under: Problems on Trains
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Q:

Two girls ate dinner together.

After that they both ordered iced tea. One girl drank them very fast and had finished five in the time it took the other to drink just one.

The girl who drank one died while the other survived. However, all of the drinks that were served turned out to contain poison.

How did the girl who drank the most survive?

Answer

The poison was in the ice. When the girl drank the iced tea, the ice was still fully frozen. Gradually, as the ice cubes melted the poison was released into the drink.

Hence, the girl who died, drunk the tea after the ice melted. So, she was died.

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Subject: Logic Puzzles Exam Prep: AIEEE , Bank Exams , CAT , GATE
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