GATE Questions and Answers with Explanation

Q:

The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number ?

A) 57	B) 75
C) 48	D) 39

Answer & Explanation Answer: D) 39

Explanation:

Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.

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Filed Under: Problems on Numbers
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Q:

How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.

A) 64	B) 63
C) 62	D) 60

Answer & Explanation Answer: B) 63

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.

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Filed Under: Permutations and Combinations
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Q:

Organisms need Nutrients in order to

A) Breaking down food	B) Utilize chemical compounds
C) recycling	D) None

Answer & Explanation Answer: A) Breaking down food

Explanation:

Nutrients are necessary for break down the food and supply energy to the organisms and to carry out essential life functions.

Important nutrients are Hydrogen, Carbon and Oxygen.

Some more important nutrients for plants are : Potassium, Sulphur, Nitrogen, Phosphorous, Calcium and Magnesium.

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Filed Under: Biology
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18 4050

Q:

A by product of involuntary muscle contraction and relaxation is

A) Oxygen	B) Water
C) Heat	D) Nitrogen

Answer & Explanation Answer: C) Heat

Explanation:

A_by_product_of_involuntary_muscle_contraction_and_relaxation_is1537166589.jpg image

When a muscle is contracted and relaxed some amount of heat is released as a by product.

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Filed Under: Chemistry
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2 4049

Q:

Rajitha has a calculator, which has 10 digits. She want to clean the calculator by removing all the keys and while reassembling it, she interchanged the locations of 3 pairs of keys. For example, if she placed the key ‘3’ in the place of the key ‘7’, she placed the key ‘7’ only in the place of the key ‘3’ and not any other key. All keys that were interchanged corresponded only to numbers. Later, she input some calculations and obtained outputs as provided in the table below. The input is shown in terms of the keys that Kavitapressed, while the output is the output displayed by the calculator.

Output:

1. 95 + 84=128
2. 128 + 64=195
3. 912 + 43=942
4. 178 + 19=192

Question :

Which of the following pair of digits is unchanged ?

A) 9, 0, 3	B) 1, 3, 8
C) 7, 0, 1	D) 2, 4, 1

Answer & Explanation Answer: C) 7, 0, 1

Explanation:

0	1	2	3	4	5	6	7	8	9
0	1	4	8	2	6	5	7	3	9

Here pairs interchanged are

2, 4

3, 8

5, 6

Unchanged are 0, 1, 7, 9

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Filed Under: Arithmetical Reasoning
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Q:

What is 70 of 50?

A) 35	B) 38
C) 42	D) 44

Answer & Explanation Answer: A) 35

Explanation:

what is 70 of 50 means 70% of 50

$\Rightarrow \frac{70 x 50}{100} = 7 x 5 = 35$

Hence, 70 of 50 is 35.

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Filed Under: Percentage
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6 4044

Q:

Directions:

Four friends Raghu, Rajesh, Ramesh and Ravi complete their Graduation in different number of years. The one who took maximum time took eight years to complete his Graduation while the one who took least time took only three years to complete it.Ravi took more time only than Raghu and completed his Graduation in five years. Ramesh did not take longer time
than Rajesh to complete his Graduation.

Question:

Who took more years to complete his graduation among all ?

A) Ramesh	B) Raghu
C) Rajesh	D) Ravi

Answer & Explanation Answer: C) Rajesh

Explanation:

Rajesh - 8 years

Ramesh - 6 or 7 years

Ravi - 5 years

Raghu - 3 years

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Filed Under: Deriving Conclusions From Passages
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Q:

Only For Geniuses

Solve this MathPuzzle if you can?

num11515666627.jpg image

Answer

Let the required number be 'X'

Condition 1 :

$\frac{X}{X} = 2 X = > 2 X^{2} = X = > X = \frac{1}{2}$

Condition 2 :

$X \times X = \frac{X}{2} = > X = \frac{1}{2}$

Therefore, $(\frac{1}{2})$ is the number which becomes double when it is divided by itself and becomes half when it is multiplied by itself.

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