GATE Questions and Answers with Explanation

Q:

Which of the following means O is a father of two children ?

A) O @ M # N	B) O # N # M
C) O @ N # M	D) N # O $ M

Answer & Explanation Answer: C) O @ N # M

Explanation:

O @ N # M means O is the father of N who is the sister of M i.e. O is a father of two children.

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Filed Under: Blood Relations
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2 3258

Q:

Which number replaces the '?' in the given series

108, 127, 2413, 2430, 41310, ?, 619875

A) 41975	B) 41325
C) 84375	D) 41365

Answer & Explanation Answer: B) 41325

Explanation:

The given series follows a pattern of +19, x19, +17, x17, +15, x15,...

Here the number which is to be replaced in ? is

41310+15=41325.

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Filed Under: Number Series
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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14 13503

Q:

Find the next number in the series 265, 269, 278, 284, ?

A) 309	B) 319
C) 298	D) 415

Answer & Explanation Answer: A) 309

Explanation:

The pattern in the given series is +4, +9, +16, +25, ... i.e. $2^{2}, 3^{2}, 4^{2}, 5^{2} . . .$

The next number is 284+25 = 309.

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Filed Under: Number Series
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8 3700

Q:

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 1155. The simple interest on the same sum for double the time at half the rate percent per annum is ?

A) Rs. 1100	B) Rs. 5500
C) Rs. 1400	D) Rs. 4120

Answer & Explanation Answer: A) Rs. 1100

Explanation:

Let the sum be Rs.x. Then,

$[x {(1 + \frac{10}{100})}^{2} - x] = 1155$

$\Rightarrow x [{(\frac{11}{10})}^{2} - 1] = 1155$

=> x =5500

sum = Rs. 5500.

So, S.I = Rs. $(\frac{5500 \times 5 \times 4}{100})$ = 1100

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Filed Under: Compound Interest
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2 5534

Q:

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate ?

A) Rs. 5422	B) Rs. 5489
C) Rs. 3972	D) Rs. 6145

Answer & Explanation Answer: C) Rs. 3972

Explanation:

Let p = Rs. 100.

Then, S.I is Rs. 50 and time = 5 years.

$∴ R = \frac{100 \times 50}{100 \times 5}$ = 10% p.a.

Now, p = Rs. 12,000 , T = 3 years and R = 10% p.a.

C.I. = Rs. $12000 \times \{{(1 + \frac{10}{100})}^{3} - 1\}$ = Rs. 3972

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Filed Under: Compound Interest
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6 8400

Q:

Statement: It is estimated that about twenty lakh people will visit the city during the ensuing festival.
Courses of action:
a. The civic authority should monitor the crowd and restrict entry of the people beyond a manageable number.
b. The local police authority should be put on high alert to maintain law and order during the festival.
c. All the hospitals in the city should be put on high alert in case of any eventuality.

A) Only a follows	B) Both b & c follows
C) Only c follows	D) Both a and b sufficient

Answer & Explanation Answer: B) Both b & c follows

Explanation:

Clearly, People cannot be deprived of enjoying the festival for lack of arrangements. Also, it becomes necessary to deploy police to regulate big crowds and avert any mishap in public gatherings. Further, it costs nothing but might prove useful to put hospitals on alert to be ready to provide quick medical aid to patients in case of any eventuality. So, both b and c follow.

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Filed Under: Statement and Courses of Action
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2 2410

Q:

If the rate increases by 2%, the simple interest received on a sum of money increases by Rs. 108. If the time period is increased by 2 years, the simple interest on the same sum increases by Rs.180. The sum is ?

A) Rs. 540	B) Rs. 415
C) Rs. 404	D) Data is not sufficient

Answer & Explanation Answer: D) Data is not sufficient

Explanation:

Let the sum be Rs. p, rate be R% p.a. and time be T years.

Then,

$(\frac{P \times T \times (R + 2)}{100}) - (\frac{P \times T \times R}{100}) = 108 \Rightarrow 2 P T = 10800 . . . . . . (1)$

And,

$(\frac{P \times R \times (T + 2)}{100}) - (\frac{P \times R \times T}{100}) = 180 \Rightarrow 2 P R = 18000 . . . . . . (2)$

Clearly, from (1) and (2), we cannot find the value of p
So, the data is not sufficient.

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Filed Under: Simple Interest
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11 12932

Q:

Question :

What is the sum which earned interest ?

Statements :

a. The total simple interest was Rs. 9000 after 9 years.
b. The total of sum and simple interest was double of the sum after 6 years.

A) Only a is sufficient	B) Neither a nor b is sufficient
C) Only b is sufficient	D) Both a and b sufficient

Answer & Explanation Answer: D) Both a and b sufficient

Explanation:

Let the sum be Rs. x

a. gives, S.I = Rs. 9000 and time = 9 years.

b. gives, Sum + S.I for 6 years = 2 x Sum

--> Sum = S.I for 6 years.

Now, S.I for 9 years = Rs. 9000

S.I for 1 year = Rs. 9000/9 = Rs. 1000.

S.I for 6 years = Rs. (1000 x 6)= Rs. 6000.

--> x = Rs. 6000

Thus, both a and b are necessary to answer the question.

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Filed Under: Simple Interest
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3 17899

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