GATE Questions

Q:

A word arrangement machine, When given an input line of words, rearranges it in every step following a certain rule. Following is an illustration of an input line of words and various steps of rearrangement.


Input: gone are take enough brought station
Step 1: take gone are enough brought station
Step 2: take are gone enough brought station
Step 3: take are station gone enough brought
Step 4: take are station brought gone enough
And Step 4 is the last step for this input. Now, find out an appropriate step in the following question following the above rule.

Question:
Input: car on star quick demand fat
What will be the third step for this input ?

A) star car demand quick on fat B) star quick car demand on fat
C) star car quick demand on fat D) none of these
 
Answer & Explanation Answer: C) star car quick demand on fat

Explanation:

Obsrving the given arrangement, we find the following pattern:
If we arrange the words in the given input in the alphabetical order and then label them as 1,2,3,4,5,6, then the last step contains the words in the order 6,1,5,2,4,3. However, the position of only one word is alteredat each step.
Input:car on star quick demand fat
Step1: star car on quick demand fat
Step2: star car quick on demand fat
Step3: star car quick demand on fat

Hence, the answer is C

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Filed Under: Sequential Output Tracing
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22 7826
Q:

The opposite of right is the opposite of

A) Left B) Wrong
C) Give D) Take
 
Answer & Explanation Answer: D) Take

Explanation:

The opposite of right is left. The opposite of left is take. And the opposite of take is give.

 

Hence, the opposite of right is the opposite of take which is left.

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34 7812
Q:

One-third of the boys and one-half of the girls of a college participated in a sport. If the number of participating students is 300, out of which 100 are boys. What is the total number of students in the college?

A) 500 B) 300
C) 600 D) 700
 
Answer & Explanation Answer: D) 700

Explanation:

Let number of boys in the school = x

Let number of girls in the school = y

Number of students participated in the sports = 300

Out of which boys = 100

but given number of boys participated in sports = x/3

=> x/3 = 100

=> x = 300

Remaining girls = 300 - 100 = 200

=> y/2 = 200

=> y = 400

Therefore, total number of students in the school = x + y = 300 + 400 = 700

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Filed Under: Percentage
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15 7805
Q:

How many number of weights do you need to weight 31 kg of Rice if you have one kg of weight stone ?

A) 3 B) 5
C) 7 D) 9
 
Answer & Explanation Answer: B) 5

Explanation:

There are total 5 ways.
we have only one kg of weight so,
2kg = 1kg + 1kg
4kg = 1 + 2 + 1
8kg = 1 + 2 + 4 + 1
16kg = 1 + 2 + 4 + 8 + 1
31kg = 1 + 2 + 4 + 8 + 16
So 5 weights are needed.

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Filed Under: Arithmetical Reasoning
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11 7778
Q:

How many balls?

Number of balls in the figure...

balls1523099634.jpg image

Answer

You have to actually count all the balls in the pyramid.
Simple way is to count the balls in each level.


So lower most level lets say 1st level has 4 x 4 balls; i.e. 16 balls
Similarly 2nd level has 3 x 3 balls; i.e. 9 balls.
3rd level has 2 x 2 balls; i.e. 4 balls.
The top most level has just 1 ball.


So the total number of balls is 16+9+4+1 = 30.


 


So the image has 30 Balls in all.

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Q:

Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what are the ages of elder and younger boys ?

A) E = 15 & Y = 3 B) E = 14 & Y = 12
C) E = 40 & Y = 22 D) E = 4 & Y = 2
 
Answer & Explanation Answer: D) E = 4 & Y = 2

Explanation:

Let the the age of the elder boy = E

 

Let the the age of the younger boy = Y

 

Given that Y = cube root of EY

 


=> Y3 = EY => E = Y2 .....(1)
By the condition of number replacement the age of the father is YE

 

The Mother's age = EY/2

 

But she is 3 years less than father => EY/2 + 3 = YE
2YE = EY + 6 ......(2)

 

Then now from the given options we can identify which satisfies the all the conditions.

 

Here Y =2 and E = 4 satisfies all the conditions.

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Filed Under: Problems on Ages
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8 7762
Q:

Which expression is equivalent to i233?

A) i B) 1
C) -i D) -1
 
Answer & Explanation Answer: A) i

Explanation:

We know that,

i2 = -1i3 = i2 x i = -1 x i = -ii4 = i2 x i2 = -1 x -1 = 1Hence, i233  =i4 x 58 + 1 = i232 x i1 = 1 x i = i

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Filed Under: Numbers
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9 7761
Q:

Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m. ?

A) 20 kmph B) 18 kmph
C) 12 kmph D) 16 kmph
 
Answer & Explanation Answer: C) 12 kmph

Explanation:

Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.

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Filed Under: Time and Distance
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7 7735