GATE Questions and Answers with Explanation

Q:

What is the right most integer of the expression $65776^{759} + 54697^{467}$ ?

A) 4	B) 6
C) 9	D) 0

Answer & Explanation Answer: C) 9

Explanation:

Last digit for the power of 6 is 6 (always)

Power cycle of 7 is 7, 9, 3, 1.

Now 467/4 gives a remainder of 3

Then the last digit is $7^{3}$ = 3

Last digit is 6 + 3 = 9.

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Filed Under: Numbers
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8 17773

Q:

8 is related to 81 in the same way as 64 is related to ____

A) 225	B) 425
C) 525	D) 625

Answer & Explanation Answer: D) 625

Explanation:

The relationship is $x^{y} : {(x + 1)}^{(y + 1)}$

Now , $64 = 4^{3}$

So, required number = ${(4 + 1)}^{(3 + 1)}$ = $5^{4}$ = 625

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Filed Under: Analogy
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129 17767

Q:

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

A) 2	B) 3
C) 4	D) 5

Answer & Explanation Answer: D) 5

Explanation:

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

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Filed Under: Numbers
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14 17741

Q:

'P' walked 1 km towards south direction and turned $90^{o}$ ACW and walked 2 km. Then he turned his left and walked 1 km and then he turned his right and walked 2 km. After that he turned $90^{o}$ ACW and walked 3 km. How far is he from the starting point ?

A) 5 km	B) 4 km
C) 2 km	D) 0 km

Answer & Explanation Answer: A) 5 km

Explanation:

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Filed Under: Direction Sense Test
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85 17729

Q:

Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is ?

A) 5	B) 4
C) 7	D) 6

Answer & Explanation Answer: A) 5

Explanation:

Let the number be x. Then,

$3 x^{2}$ - 4x = x + 50

$3 x^{2}$ - 5x - 50 = 0

(3x + 10)(x - 5) = 0

x = 5

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Filed Under: Arithmetical Reasoning
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16 17722

Q:

A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

A) 32 kmph	B) 20 kmph
C) 18 kmph	D) 24 kmph

Answer & Explanation Answer: D) 24 kmph

Explanation:

Let the total distance of the journey of a man = d kms

Now, the average speed of the entire journey = $\frac{d}{\frac{d}{120} + \frac{d}{120} + \frac{d}{40}}$ = 24 kmph.

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Filed Under: Time and Distance
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30 17702

Q:

The simple interest on Rs.10 for 4 months at the rate of 3 paise per month is

A) 0.3 Paise	B) 1.2 Paise
C) 30 Paise	D) 3 Paise

Answer & Explanation Answer: B) 1.2 Paise

Explanation:

Given Principal amount P = Rs. 10

Time T = 4 months

Rate of interest R = 3 ps

Interest I = PTR/100 = (10 x 4 x 3)/100 = 12/10 = 1.2 paise.

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Filed Under: Simple Interest
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7 17688

Q:

If yesterday were tomorrow, then today would be Friday. What day is today?

A) Saturday	B) Monday
C) Sunday	D) Tuesday

Answer & Explanation Answer: C) Sunday

Explanation:

If yesterday were tomorrow, today is Friday => tomorrow of friday is Saturday.

Hence, it implies that today is Sunday if tomorrow is Saturday.

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Filed Under: Calendar
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86 17664

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