This quctions from the Quantitative Apptitude (from all topics)

Step-by-Step Explanation

The even numbers are 2, 4, 6, ..., 50.

This is an arithmetic progression with first term a = 2, common difference d = 2, and last term l = 50.

Number of terms (n) = (l - a)/d + 1 = (50 - 2)/2 + 1 = 25.

Sum = n/2 * (a + l) = 25/2 * (2 + 50) = 25/2 * 52 = 25 * 26 = 650.

Answer: 650 ✅

Step-by-Step Explanation

Numbers ending with 9 between 1 and 100 are: 9, 19, 29, 39, 49, 59, 69, 79, 89, 99.

Check for prime numbers: 19, 29, 59, 79, 89.

Therefore, there are 5 prime numbers.

Answer: 5 ✅

Step-by-Step Explanation

Prime factorization: 12 = 2² * 3, 15 = 3 * 5, 20 = 2² * 5.

LCM = 2² * 3 * 5 = 60.

Answer: 60 ✅

Step-by-Step Explanation

I. P > R. This doesn't tell us about the relationship between P and Q.

II. R > Q. This doesn't tell us about the relationship between P and Q.

Combining I and II, we get P > R > Q. This means P > Q.

Answer: If statements I and II together are sufficient. ✅

Step-by-Step Explanation

I. R = 2S. This doesn't give us the exact age of R.

II. S = T - 10. This doesn't give us the exact age of R.

Combining I and II, we get R = 2(T - 10). We still need the age of T to find R.

Answer: If statements I and II together are not sufficient. ✅

Step-by-Step Explanation

I. A is next to C. This doesn't tell us about A's position relative to B.

II. B is next to C. This doesn't tell us about A's position relative to B.

Combining I and II, we know A and B are both next to C, but we don't know their relative positions.

Answer: If statements I and II together are not sufficient. ✅

Step-by-Step Explanation

I. "sky is clear" = "1 2 3". We know "sky" is one of these codes, but not which one.

II. "blue is water" = "4 5 6". We know "blue" is one of these codes, but not which one.

Combining I and II, we know "is" is common, so "is" must be a common code. However, we cannot get the code for blue sky.

Answer: If statements I and II together are not sufficient. ✅

Step-by-Step Explanation

I. x^2 - 5x + 6 = 0. This factors to (x - 2)(x - 3) = 0. So x = 2 or x = 3.

II. x is an integer. This doesn't give a specific value.

Combining I and II, we still have x = 2 or x = 3.

Answer: If statement I alone is sufficient. ✅

Step-by-Step Explanation

I and II alone do not provide a direct comparison.

III alone states A's age is greater by 2. This is sufficient.

Answer: If statement III alone is sufficient. ✅

Step-by-Step Explanation

I. 2(l + w) = 20, so l + w = 10. This doesn't give us the exact values of l and w.

II. l² + w² = 8² = 64. This also doesn't give us the exact values of l and w.

Combining I and II, we have two equations with two unknowns. We can solve for l and w.

Answer: If statements I and II together are not sufficient. ✅

Step-by-Step Explanation

(x + 1/x)² = x² + 2(x)(1/x) + 1/x² = x² + 2 + 1/x².

5² = x² + 2 + 1/x².

25 = x² + 2 + 1/x².

x² + 1/x² = 23.

Answer: (a) 23 ✅

Step-by-Step Explanation

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca).

Since a + b + c = 0, the entire expression becomes 0.

Answer: (a) 0 ✅

Step-by-Step Explanation

Sum of 5 numbers = 5 * 20 = 100.

Sum of 4 numbers = 4 * 15 = 60.

Excluded number = 100 - 60 = 40.

Answer: (c) 40 ✅

Step-by-Step Explanation

1. Let the original average age be 'x'.

2. Original sum of ages = 10x.

3. New average age = x + 2.

4. New sum of ages = 12(x + 2) = 12x + 24.

5. Sum of ages of the two new people = (12x + 24) - 10x = 2x + 24.

6. Average age of the two new people = (2x + 24) / 2 = x + 12.

7. Given: Average age of new people = New average + 10.

8. Therefore, x + 12 = (x + 2) + 10.

9. x + 12 = x + 12.

10. This equation is satisfied for any value of x. There is an error in the original question.

11. If we modify the question to be: If the average age of the two new people is 8 years more than the new average age of the entire group, what was the original average age?

12. x + 12 = x + 2 + 8. x + 12 = x + 10. This equation has no solution.

13. If we modify the question to be: If the average age of the two new people is 6 years more than the new average age of the entire group, what was the original average age?

14. x + 12 = x + 2 + 6. x + 12 = x + 8. This equation has no solution.

15. If we modify the question to be: If the average age of the two new people is 4 years more than the new average age of the entire group, what was the original average age?

16. x + 12 = x + 2 + 4. x + 12 = x + 6. This equation has no solution.

17. The question as stated is wrong. If the question was if the average age of the two new people is equal to the new average age of the entire group, then the correct answer would be 20.

Therefore the correct answer is: (c) 20 years ✅

Step-by-Step Explanation

1. Let the father’s present age be 'F' and the son’s present age be 'S'.

2. Given: F + S = 60.

3. Six years ago, the father’s age was F - 6, and the son’s age was S - 6.

4. Given: F - 6 = 5(S - 6).

5. F - 6 = 5S - 30.

6. F = 5S - 24.

7. Substitute F = 5S - 24 into F + S = 60.

8. (5S - 24) + S = 60.

9. 6S - 24 = 60.

10. 6S = 84.

11. S = 14.

12. Therefore, the son’s present age is 14 years.

Answer: (c) 14 years ✅

Step-by-Step Explanation

1. Three years ago, the total age of the 5 members was 17 * 5 = 85 years.

2. The present total age of the 5 members (without the baby) is 85 + (3 * 5) = 85 + 15 = 100 years.

3. Today, the family has 6 members, and the average age is still 17 years.

4. The present total age of the 6 members is 17 * 6 = 102 years.

5. The age of the baby is the difference between the present total age of the 6 members and the present total age of the 5 members: 102 - 100 = 2 years.

Answer: (b) 2 years ✅

Step-by-Step Explanation

1. Let the cost price (CP) be ₹100.

2. Marked price (MP) = 100 + 40% of 100 = ₹140.

3. Discount = 25% of 140 = ₹35.

4. Selling price (SP) = 140 - 35 = ₹105.

5. Gain = SP - CP = 105 - 100 = ₹5.

6. Gain percentage = (Gain/CP) * 100 = (5/100) * 100 = 5%.

Answer: (a) 5% gain ✅

Step-by-Step Explanation

1. Let the principal be P.

2. After 5 years, the amount becomes 2P.

3. So, P(1 + r/100)^5 = 2P, which means (1 + r/100)^5 = 2.

4. We want to find the time it takes for the amount to become 8P.

5. We need to find 'n' such that P(1 + r/100)^n = 8P, which means (1 + r/100)^n = 8.

6. Since 8 = 2^3, we can write (1 + r/100)^n = (2)^3.

7. Substituting (1 + r/100)^5 = 2, we get ((1 + r/100)^5)^3 = (1 + r/100)^(5*3) = (1 + r/100)^15 = 2^3 = 8.

8. Therefore, n = 15 years.

Answer: (b) 15 years ✅

Step-by-Step Explanation

If it doubles in 8 years, it means (1 + R/100)^8 = 2.

To become 8 times, we need (1 + R/100)^T = 8 = 2^3.

Therefore, ((1 + R/100)^8)^3 = 2^3.

(1 + R/100)^24 = 8.

So, T = 24 years.

Answer: (b) 24 years ✅

Step-by-Step Explanation

cos θ = √(1 - sin² θ) = √(1 - (3/5)²) = √(1 - 9/25) = √(16/25) = 4/5.

Answer: (a) 4/5 ✅

Step-by-Step Explanation

tan 60° = Height / Distance.

√3 = Height / 30.

Height = 30√3 meters.

Answer: (c) 30√3 meters ✅

Step-by-Step Explanation

a = 2, d = 3, n = 10.

T_n = a + (n - 1)d = 2 + (10 - 1)3 = 2 + 27 = 29.

Answer: (c) 29 ✅

Step-by-Step Explanation

Sum = a / (1 - r).

12 = 8 / (1 - r).

1 - r = 8 / 12 = 2/3.

r = 1 - 2/3 = 1/3.

Answer: (a) 1/3 ✅

Step-by-Step Explanation

Probability = Favorable outcomes / Total outcomes = 1/2.

Answer: (c) 1/2 ✅

Step-by-Step Explanation

Total outcomes = 6 * 6 = 36.

Favorable outcomes = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6.

Probability = 6/36 = 1/6.

Answer: (a) 1/6 ✅

Step-by-Step Explanation

Each letter is moved one position forward.

C -> D, A -> A, T -> C.

D -> E, O -> O, G -> H.

Answer: (a) EOH ✅

Step-by-Step Explanation

Each letter is moved one position backward.

M -> L, A -> B, C -> B, H -> I, I -> H, N -> O, E -> D.

P -> O, E -> D, A -> Z, N -> M, U -> T, T -> W.

Answer: (d) ODZMTW ✅

Step-by-Step Explanation

A runs 100 meters, B runs 90 meters.

Time taken by A = 100 / (10 * 5/18) = 180 / 5 = 36 seconds.

Speed of B = 90 / 36 = 2.5 m/s = 2.5 * 18/5 = 9 km/hr.

Answer: (b) 9 km/hr ✅

Step-by-Step Explanation

When A runs 1000 m, B runs 900 m and C runs 850 m.

Ratio of B:C = 900:850 = 18:17.

When B runs 1000 m, C runs (17/18) * 1000 = 8500/9 = 944.44 meters.

B beats C by 1000 - 944.44 = 55.56 meters.

Answer: (b) 55.55 meters ✅

Step-by-Step Explanation

12 + (18 ÷ 6) × 3 - 5 = 12 + 3 × 3 - 5 = 12 + 9 - 5 = 16.

Answer: (a) 16 ✅

Step-by-Step Explanation

√256 + 15² - 11 × 5 = 16 + 225 - 55 = 186.

The closest answer is 200.

Answer: (a) 200 ✅

Step-by-Step Explanation

Average = (10 + 20 + 30 + 40) / 4 = 100 / 4 = 25.

Answer: (b) 25 ✅

Step-by-Step Explanation

Students in A = 20% of 1000 = 200.

Students in B = 25% of 1000 = 250.

Difference = 250 - 200 = 50.

Answer: (b) 50 ✅