Simplification Practice Test Questions - Quantitative Aptitude -- Free Practice

Question 1

A*B implies A²+B². What is the value of 6*(2*4)?

A

999✓✗

B

3616✓✗

C

324✓✗

D

436✓✗

Explanation

A*B = A² + B². First 2*4 = 4 + 16 = 20.
Then 6*20 = 36 + 400 = 436.

Question 2

Ramesh spends 40% of his monthly salary on food, 40% of the remaining on conveyance and clothes and saves 50% of the remaining amount. If his monthly salary is Rs.17,000, how much money does he save every month ?

A

Rs. 3,400✓✗

B

Rs. 3060✓✗

C

Rs. 2,540✓✗

D

Rs.1,880✓✗

Explanation

After food: 17000 × 60% = Rs. 10,200. The amount spent on conveyance and clothes = 40% of 10,200 = Rs. 4,080, leaving Rs. 6,120.
Savings = 50% of 6,120 = Rs. 3,060.

Question 3

Rohan's income doubles after every one year. If the initial income was Rs. 4 lakhs, What would be the income after 6 years?

A

Rs. 2.24 crores✓✗

B

Rs. 2.28 crores✓✗

C

Rs. 2.52 crores✓✗

D

Rs. 2.56 crores✓✗

Explanation

The income doubles every year, so after 6 years it is 4 lakh x 2⁶ = 4 × 64 = 256 lakh = Rs. 2.56 crores.

Question 4

38 of 168 * 15 / 5 + X = 549 / 9 + 275

A

107✓✗

B

147✓✗

C

10✓✗

D

296✓✗

Explanation

38 of 168 = 63. Then 63 × 155 = 63 × 3 = 189.
5499 + 275 = 61 + 275 = 336.
X = 336 - 189 = 147.

Question 5

What will come in place of the question mark (?) in the following question?

112.36 + 225.05 + ? = 815.30

A

474.46✓✗

B

477.89✓✗

C

524.41✓✗

D

564.40✓✗

Explanation

? = 815.30 - 112.36 - 225.05 = 815.30 - 337.41 = 477.89.

Question 6

Find the value of the sum of reciprocals of surds.

A

0✓✗

B

3✓✗

C

-3✓✗

D

1✓✗

Explanation

Rationalising, 1√n + √n + 1 = √n + 1 - √n. The sum then telescopes: (√2 - 1) + (√3 - √2) + ... + (√16 - √15) = √16 - 1.
= 4 - 1 = 3.

Question 7

Simplify (brackets with a bar over some terms).

A

2✓✗

B

1✓✗

C

-3✓✗

D

5✓✗

Explanation

The bar covers 12 - 52 = -2, so 2 - (-2) = 4.
1 + 4 = 5, then 3 - 5 = -2, then 2 × (-2) = -4.
1 + (-4) = -3.

Question 8

Evaluate (nested roots and decimals).

A

1✓✗

B

10✓✗

C

100✓✗

D

1000✓✗

Explanation

√0.0064 = 0.08, so 0.01 + 0.08 = 0.09, and √0.09 = 0.3.
Denominator = 0.01 × 0.3 = 0.003.
Value = 0.30.003 = 100.

Question 9

Find the value (square root and cube roots).

A

9✓✗

B

250✓✗

C

1.072✓✗

D

1.060✓✗

Explanation

√0.0016 = 0.04, the cube root of 8000000 = 200, the cube root of 0.000512 = 0.08 and the cube root of 0.064 = 0.4.
Value = 0.04 × 2000.08 × 0.4 = 80.032 = 250.

Question 10

The value of 25.25 – 23.23 + 24.24 is

A

26✓✗

B

26.26✓✗

C

2.2✓✗

D

-22.22✓✗

Explanation

25.25 - 23.23 + 24.24 = 2.02 + 24.24 = 26.26.

Question 11

What is the value of (40.25 ÷ 5) + (0.07 × 5)(0.15 × 8) + (0.18 ÷ 0.2)

A

7.5✓✗

B

3✓✗

C

5✓✗

D

4✓✗

Explanation

The numerator = 8.05 + 0.35 = 8.4 and the denominator = 1.2 + 0.9 = 2.1.
The value = 8.42.1 = 4.

Question 12

Simplify: 0.72 × 0.72 × 0.72 - 0.39 × 0.39 × 0.390.72 × 0.72 + 0.72 × 0.39 + 0.39 × 0.39

A

0.333✓✗

B

0.33✓✗

C

0.3333✓✗

D

0.3334✓✗

Explanation

Using a³ - b³ = (a - b)(a² + ab + b²), the expression = a - b = 0.72 - 0.39 = 0.33.

Question 13

If 1²+2²+3²+…..+ 10² = 385, then 3²+6²+9²+….+30² is equal to

A

3465✓✗

B

2310✓✗

C

1155✓✗

D

770✓✗

Explanation

3² + 6² + 9² + ... + 30² = 3²(1² + 2² + 3² + ... + 10²) = 9 × 385 = 3465.

Question 14

If a*b = 2a+3b, then the value of 2*3 + 3*4 is

A

24✓✗

B

31✓✗

C

32✓✗

D

34✓✗

Explanation

a * b = 2a + 3b.
2 * 3 = 2 × 2 + 3 × 3 = 13 and 3 * 4 = 2 × 3 + 3 × 4 = 18.
2 * 3 + 3 * 4 = 13 + 18 = 31.

Question 15

What is the value of .1 × .1 × .1 + .02 × .02 × .02.2 × .2 × .2 + .04 × .04 × .04

A

0.0125✓✗

B

0.125✓✗

C

0.25✓✗

D

0.5✓✗

Explanation

The numerator = 0.1³ + 0.02³ and the denominator = 0.2³ + 0.04³ = 2³ × (0.1³ + 0.02³).
The value = 18 = 0.125.

Question 16

On simplification of the following, the result will be
(1 - 12)(1 - 13)(1 - 14)……..(1 - 1100)

A

0.01✓✗

B

0.001✓✗

C

1✓✗

D

0.1✓✗

Explanation

(1 - 12)(1 - 13)...(1 - 1100) = 12 × 23 × 34 × ... × 99100.
The terms cancel, leaving 1100 = 0.01.

Question 17

What is the value of 0.125 + 0.0270.5 × 0.5 + 0.09 - 0.15

A

1✓✗

B

0.2✓✗

C

0.08✓✗

D

0.8✓✗

Explanation

0.125 = 0.5³ and 0.027 = 0.3³. The denominator = 0.5² + 0.3² - 0.5 × 0.3 = 0.25 + 0.09 - 0.15.
Using a³ + b³ = (a + b)(a² - ab + b²), the value = a + b = 0.5 + 0.3 = 0.8.

Question 18

What is value of (13.8 × 1.9 ÷ 5.7 + 11.2 of (116) - (120))?

A

5.50✓✗

B

5.225✓✗

C

55.22✓✗

D

5.25✓✗

Explanation

13.8 × 1.9 ÷ 5.7 = 26.22 ÷ 5.7 = 4.6. 11.2 of 116 = 11.216 = 0.7.
Value = 4.6 + 0.7 - 120 = 5.3 - 0.05 = 5.25.

Question 19

In a class, there are some girls and boys. One day, 30 boys leave the class, so there were 4 girls for each boy. After some time, on the same day, 175 girls leave the class. Then, there were 2 boys for each girl. How much would be double the number of boys originally present in the class?

A

225✓✗

B

193✓✗

C

160✓✗

D

None of these✓✗

Explanation

Let the girls be g and the boys be b. After 30 boys leave, g = 4(b - 30).
After 175 girls leave, b - 30 = 2(g - 175).
Substitute g = 4b - 120: b - 30 = 2(4b - 295) = 8b - 590, so 7b = 560 and b = 80.
Double the number of boys = 160.

Question 20

Pune’s population starts decreasing from 272000 at the rate of 2700 per year. Satara’s population starts increasing at the same time from 190000 at the rate of 1400 per year. When will both the cities have same population?

A

15 years✓✗

B

20 years✓✗

C

10 years✓✗

D

16 years✓✗

Explanation

After t years: 272,000 - 2700t = 190,000 + 1400t.
82,000 = 4100t, so t = 20 years.

Question 21

A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get?

A

18 pounds✓✗

B

20 pounds✓✗

C

25 pounds✓✗

D

30 pounds✓✗

Explanation

150 pounds at Rs. 70 per pound = Rs. 10,500.
He spends Rs. 9060, so the remaining amount = Rs. 1440.
At Rs. 72 per pound, he gets 144072 = 20 pounds.

Question 22

3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other three?

A

(A + B)² - 4AB✓✗

B

(A – B)² + 4AB✓✗

C

A² + B² - 4AB + 2AB✓✗

D

A² – B² + 2B(B – A)✓✗

Explanation

(A + B)² - 4AB = (A - B)². A² + B² - 4AB + 2AB = A² + B² - 2AB = (A - B)². A² - B² + 2B(B - A) = A² - B² + 2B² - 2AB = (A - B)².
(A - B)² + 4AB = (A + B)², which is different from the other three.

Question 23

Find the value of (X) in the given equation ?

35% of 1500 + X = 45% of 4200 – 320

A

910✓✗

B

980✓✗

C

1012✓✗

D

1045✓✗

Explanation

35% of 1500 = 525 and 45% of 4200 = 1890.
525 + X = 1890 - 320 = 1570, so X = 1570 - 525 = 1045.

Question 24

Out of the three numbers A, B and C, A exceeds B by 20 and C exceeds A by 55. If the sum of all the numbers is 230, What is the difference between the largest and the smallest number?

A

52✓✗

B

58✓✗

C

63✓✗

D

75✓✗

Explanation

Let B = b. Then A = b + 20 and C = A + 55 = b + 75.
The sum = b + b + 20 + b + 75 = 3b + 95 = 230, so b = 45, A = 65 and C = 120.
The difference between the largest and the smallest = 120 - 45 = 75.

Question 25

A bonus of Rs.2800 is to be divided among 3 people such that Alex gets twice as much as David, who receives one-fourth as much as Peter. What amount did Peter get?

A

1200✓✗

B

2000✓✗

C

1600✓✗

D

1500✓✗

Explanation

Let David get x. Alex gets 2x. David gets one-fourth of Peter's amount, so Peter gets 4x.
x + 2x + 4x = 7x = 2800, so x = 400.
Peter gets 4 × 400 = Rs. 1600.