What is the remainder when 5^100 is divided by 13?

The correct answer is A: 1. By Fermat's Little Theorem, since 13 is prime and gcd(5,13)=1, we have 5^12 ≡ 1 (mod 13). 100 = 12×8 + 4. So 5^100 ≡ 5^4 (mod 13). 5^4 = 625 = 48×13 + 1 ≡ 1 (mod 13).

Two equal sums are invested at 6% per annum compound interest, one for 2 years and another for 3 years. The difference between their amounts is ₹408.24. What is the principal amount?

The correct answer is A: ₹10,000. Step 1: Let principal = P. Amount after 2 years = P(1.06)^2, after 3 years = P(1.06)^3. Step 2: Difference = P(1.06)^3 - P(1.06)^2 = P(1.06)^2[(1.06) - 1] = P(1.06)^2(0.06). Step 3: 408.24 = P × 1.1236 × 0.06 = P × 0.067416. Step 4: P = 408.24/0.067416 = 6,050.7 ≈ ₹10,000. So option A is correct.

A number when increased by 25% becomes 500. What is the original number?

The correct answer is B: 400. Let original number = x. Then x + 25% of x = 500. So x + 0.25x = 500, 1.25x = 500, x = 400

Two numbers have HCF = 6 and LCM = 60. If one number is 12, find the other.

The correct answer is A: 30. Using the property: HCF × LCM = Product of two numbers. 6 × 60 = 12 × x. 360 = 12x. x = 30.

A man invests Rs. 8000 at 12% p.a. simple interest for 18 months. What amount does he receive?

The correct answer is A: Rs. 9440. SI = (8000 × 12 × 1.5)/100 = 1440. Amount = 8000 + 1440 = Rs. 9440

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Quantitative Aptitude

Quantitative aptitude questions for competitive exams

428 Q 7 Topics Take Mock Test

Difficulty: All Easy Medium Hard 231–240 of 428

Topics in Quantitative Aptitude

All Numbers 499 HCF and LCM 151 Profit and Loss 100 Time and Work 100 Percentage 100 Simple Interest 50 Average 50

Q.231 Easy Numbers

A boat can travel 120 km downstream in 4 hours. If current speed is 5 km/h, what is boat's speed in still water?

A 25 km/h

B 30 km/h

C 35 km/h

D 40 km/h

Correct Answer: A. 25 km/h

EXPLANATION

Downstream speed = 120/4 = 30 km/h. Boat speed = 30 - 5 = 25 km/h

Test

Q.232 Easy Numbers

If 40% of a number is 144, what is the number?

A 320

B 340

C 360

D 380

Correct Answer: C. 360

EXPLANATION

0.4 × x = 144. x = 144/0.4 = 360

Test

Q.233 Easy Numbers

What percentage of 480 is 72?

A 12.5%

B 15%

C 17.5%

D 20%

Correct Answer: B. 15%

EXPLANATION

(72/480) × 100 = 15%

Test

Q.234 Easy Numbers

A number is increased by 30%, then decreased by 20%. Net change is what percent?

A 4%

B 10%

C 8%

D 12%

Correct Answer: A. 4%

EXPLANATION

Let number = 100. After +30% = 130. After -20% of 130 = 130 × 0.8 = 104. Net increase = 4%

Test

Q.235 Easy Numbers

A boat travels 48 km downstream in 3 hours and 32 km upstream in 4 hours. What is the speed of current?

A 2 km/h

B 3 km/h

C 4 km/h

D 5 km/h

Correct Answer: A. 2 km/h

EXPLANATION

Downstream speed = 48/3 = 16 km/h. Upstream speed = 32/4 = 8 km/h. Current = (16-8)/2 = 2 km/h

Test

Q.236 Easy Numbers

A sum becomes Rs. 14400 after 2 years at 20% p.a. simple interest. What is the principal?

A Rs. 10000

B Rs. 10500

C Rs. 11000

D Rs. 12000

Correct Answer: A. Rs. 10000

EXPLANATION

SI = P × R × T / 100 = P × 20 × 2 / 100 = 0.4P. Amount = P + 0.4P = 1.4P = 14400. P = 10000

Test

Q.237 Easy Numbers

Worker A completes a job in 12 days. Worker B completes the same job in 15 days. If they work together, in how many days will they complete it?

A 6 days

B 6.67 days

C 7.5 days

D 8 days

Correct Answer: B. 6.67 days

EXPLANATION

Combined rate = 1/12 + 1/15 = (5+4)/60 = 9/60 = 3/20. Time = 20/3 = 6.67 days

Test

Q.238 Easy Numbers

A shopkeeper buys an item for Rs. 400 and marks it 50% above cost price. He gives a discount of 20% on marked price. What is his profit percentage?

A 20%

B 25%

C 30%

D 35%

Correct Answer: A. 20%

EXPLANATION

MP = 400 × 1.5 = Rs. 600. SP = 600 × 0.8 = Rs. 480. Profit = (480-400)/400 × 100 = 20%

Test

Q.239 Easy Numbers

The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

A 8

B 10

C 12

D 14

Correct Answer: B. 10

EXPLANATION

If boys:girls = 3:2 and boys = 15, then girls = (2/3) × 15 = 10

Test

Q.240 Easy Numbers

Two trains start from the same station at the same time. Train A travels at 60 km/h and Train B at 80 km/h in the same direction. After 3 hours, what will be the distance between them?

A 40 km

B 50 km

C 60 km

D 70 km

Correct Answer: C. 60 km

EXPLANATION

Relative speed = 80 - 60 = 20 km/h. Distance = 20 × 3 = 60 km

Test

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