GATE Exam Practice Test

QR #5

Speed and Distance Problem (basic level)

A delivery truck travels from the warehouse to a shop at an average speed of 60 km per hour. The journey takes exactly 40 minutes.

On the return trip from the shop back to the warehouse (same route), the truck travels at an average speed of 40 km per hour due to heavy traffic.

How long does the return journey take?
A) 40 minutes
B) 50 minutes
C) 60 minutes
D) 80 minutes

Answer: C) 60 minutes

Solution:
Step 1: Find the distance between warehouse and shop

Speed to shop: 60 km/hour
Time taken: 40 minutes = 40/60 hours = 2/3 hours
Distance = Speed × Time
Distance = 60 × 2/3 = 40 km

Step 2: Calculate return journey time

Same distance: 40 km
Return speed: 40 km/hour
Time = Distance ÷ Speed
Time = 40 ÷ 40 = 1 hour
Convert to minutes: 1 × 60 = 60 minutes

The return journey takes 60 minutes (or 1 hour)

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Quantitative Reasoning #4

A Year 6 class sells handmade bookmarks to raise money for their graduation trip. They spend $45 on materials to make 80 bookmarks. They sell 65 bookmarks for $1.50 each.

After the sale ends, they donate the remaining unsold bookmarks to the library. A parent then offers to buy all those donated bookmarks from the library for $1 each and gives that money back to the class fundraiser.

What is the total profit the class makes from this fundraiser?

A) $67.50
B)$72.50
C) $82.50
D) $97.50

Answer: A) $67.50

Solution:

Step 1: Calculate revenue from initial sale:-
Bookmarks sold: 65
Price per bookmark: $1.50
Revenue from sale: 65 × $1.50 = $97.50

Step 2: Calculate revenue from donated bookmarks:-
Total bookmarks made: 80
Bookmarks sold: 65
Bookmarks donated: 80 - 65 = 15 bookmarks
Parent buys at $1 each: 15 × $1 = $15.00

Step 3: Calculate total profit:-
Total revenue: $97.50 + $15.00 = $112.50
Total costs: $45.00
Profit = $112.50 - $45.00 = $67.50

The class makes a profit of $67.50.

Quote 1:

“Education is the most powerful weapon which you can use to change the world.”
— Nelson Mandela

Question 1: Why does Mandela describe education as a “weapon”?

A) Education should be used to fight against other people
B)Education is dangerous and should be controlled carefully
C) Education is a powerful tool that can transform society
D) Education is only useful in times of conflict

Correct Answer: C - Mandela uses “weapon” metaphorically to emphasize education’s power to create change, not as something violent but as a force for positive transformation.

Quantitative Reasoning #4

A school is building a rectangular playground that is 24 meters long and 16 meters wide. They want to put a fence around three sides only - the two long sides and one short side. The fourth side (one short side) connects to the school building, so no fence is needed there.

Additionally, they need to leave a 3-meter gap on one of the long sides for a gate entrance.
What is the total length of fencing needed?
A) 58 meters
B)61 meters
C) 64 meters
D) 67 meters

Answer: 61 meters

Solution:

Step 1: Calculate fence needed for three sides (without the gate gap)

Two long sides: 24 + 24 = 48 meters
One short side: 16 meters
48 + 16 = 64 meters

Step 2: Subtract the 3-meter gate gap:
Total fencing = 64 - 3 = 61 meters

Quantitative Reasoning #3

A balance scale is perfectly balanced. On the left side, there are 3 identical boxes and 5 loose marbles. On the right side, there are 2 identical boxes (same as the left) and 17 loose marbles.

How many marbles does each box contain?
A) 8 marbles
B) 10 marbles
C) 12 marbles
D) 14 marbles

Answer: C) 12 marbles

Solution:

Let each box = b marbles
Left side: 3b + 5
Right side: 2b + 17

Since the scale is balanced:
3b + 5 = 2b + 17

Subtract 2b from both sides:
3b - 2b + 5 = 17
b + 5 = 17

Subtract 5 from both sides:
b = 12

Each box contains 12 marbles.

Quantitative Reasoning #2

At a class party, there are 20 pizza slices on a table: 7 slices have pepperoni only, 5 slices have mushrooms only, 6 slices have both pepperoni AND mushrooms, and 2 slices are plain cheese.

If Marcus randomly picks one slice without looking, what is the probability he gets a slice that has pepperoni on it (either by itself or with mushrooms)?

A) 35%
B)55%
C) 60%
D) 65%

Quantitative Reasoning #1

A school is organizing a fundraising event. They have 156 books to distribute equally into gift baskets. Each basket must contain the same number of books, and they want to make between 10 and 20 baskets. After filling all the baskets completely, they have 12 books remaining.

How many books are in each basket?
A) 10 books
B)12 books
C) 13 books
D) 16 books

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