GAT Quantitative Reasoning 3 — Questions and Answers

Question 1: If 3x + 7 = 22, what is the value of 6x + 14?

30
44 (Correct answer)
37
52

Correct answer: 44

From 3x + 7 = 22, we get 3x = 15. The expression 6x + 14 = 2(3x + 7) = 2 × 22 = 44.

Rather than solving for x first, recognize that 6x + 14 = 2(3x + 7). Since 3x + 7 = 22, then 6x + 14 = 2 × 22 = 44. This algebraic shortcut saves time. Alternatively: 3x = 15, so x = 5, then 6(5) + 14 = 30 + 14 = 44.

Question 2: A store offers a 20% discount on a shirt priced at 150 SAR. After the discount, a 15% VAT is added. What is the final price?

120 SAR
138 SAR (Correct answer)
127.50 SAR
142.50 SAR

Correct answer: 138 SAR

After 20% discount: 150 × 0.80 = 120 SAR. After 15% VAT: 120 × 1.15 = 138 SAR.

Step 1: Calculate the discounted price. 20% of 150 = 30, so discounted price = 150 - 30 = 120 SAR. Step 2: Apply 15% VAT on the discounted price. 15% of 120 = 18, so final price = 120 + 18 = 138 SAR. A common mistake is applying VAT before the discount or on the original price.

Question 3: What is the next number in the sequence: 2, 6, 18, 54, ___?

108
162 (Correct answer)
72
216

Correct answer: 162

Each number is multiplied by 3 to get the next: 2×3=6, 6×3=18, 18×3=54, 54×3=162.

This is a geometric sequence with a common ratio of 3. Each term is obtained by multiplying the previous term by 3: 2→6→18→54→162. To verify: 6/2=3, 18/6=3, 54/18=3. Therefore the next term is 54×3=162.

Question 4: If the average of five numbers is 24, and four of the numbers are 18, 22, 26, and 30, what is the fifth number?

20
24 (Correct answer)
28
22

Correct answer: 24

The sum of all five numbers = 24 × 5 = 120. The sum of the four known numbers = 18 + 22 + 26 + 30 = 96. The fifth number = 120 - 96 = 24.

Average = Sum ÷ Count, so Sum = Average × Count = 24 × 5 = 120. The four known numbers sum to 18 + 22 + 26 + 30 = 96. Therefore, the fifth number = 120 - 96 = 24. This is a standard GAT technique: use the average formula to find a missing value.

Question 5: A car travels 240 km in 3 hours. If it increases its speed by 20 km/h, how long will it take to travel 360 km?

3 hours
3.6 hours (Correct answer)
4 hours
4.5 hours

Correct answer: 3.6 hours

Original speed = 240/3 = 80 km/h. New speed = 80 + 20 = 100 km/h. Time = 360/100 = 3.6 hours.

Step 1: Original speed = distance ÷ time = 240 ÷ 3 = 80 km/h. Step 2: New speed = 80 + 20 = 100 km/h. Step 3: Time for new journey = distance ÷ speed = 360 ÷ 100 = 3.6 hours (or 3 hours and 36 minutes). This tests the fundamental relationship: speed = distance/time.

Question 6: What is 25% of 60% of 400?

40
60 (Correct answer)
80
100

Correct answer: 60

60% of 400 = 240. 25% of 240 = 60.

This is a chained percentage problem. First: 60% of 400 = 0.60 × 400 = 240. Then: 25% of 240 = 0.25 × 240 = 60. Alternatively, multiply the percentages: 0.25 × 0.60 = 0.15, then 0.15 × 400 = 60. Both methods give the same answer.

GAT Quantitative Reasoning 3

If 3x + 7 = 22, what is the value of 6x + 14?