Directions(1-5): Simplification Questions
1. 40% of 375 ÷ [latex]\sqrt[3]{512}[/latex]× 30 = 4500 ÷ ?

A. 8 B. 10 C. 9 D. 12

Answer: Option A
Explanation: 40% of 375 ÷ [latex]\sqrt[3]{512}[/latex]× 30 = 4500 ÷ ? 150 ÷ 8 × 30 = 4500 ÷ ? ? = 4500 × 8 ÷ 150 ÷ 30 ? = 8
2. What should come at the place of Question mark (?) in the following question? [latex]{?}{^3}[/latex] – 300 – 43 + 4 = 148 ÷ 37

A. 12 B. 7 C. 5 D. 12

Answer: Option B
Explanation: [latex]{?}{^3}[/latex] – 300 – 43 + 4 = 148 ÷ 37 [latex]{?}^{3}[/latex] – 343 + 4 = 4 [latex]{?}^{3}[/latex] = 343 ? = 7
3. What should come at the place of Question mark (?) in the following question? 299 ÷ [latex]\sqrt{169}[/latex] x 11 - [latex]\sqrt{361}[/latex] = [latex]{?}^{2}[/latex] + 38

A. 11 B. 8 C. 16 D. 14

Answer: Option D
Explanation: [latex]\frac{299}{\sqrt{169}}[/latex] x 11 - [latex]\sqrt{361}[/latex] = [latex]{?}^{2}[/latex] + 38 [latex]\frac{299}{13}[/latex] x 11 – 19 – 38 = [latex]{?}^{2}[/latex] 253 – 57 = [latex]{?}^{2}[/latex] [latex]{?}^{2}[/latex] = 196 ? = 14
4.What should come at the place of Question mark (?) in the following question? 42.5% of 750 = ?% of 43 – 26% of ?

A. 1525 B. 2152 C. 1850 D. 1875

Answer: Option D
Explanation: From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.42.5% of 750 = ?% of 43 – 26% of ? 85% of 375 = [latex]\frac{43 × ? - 26 × ?}{100}[/latex] 85% of 375 = 17 x [latex]\frac{?}{100}[/latex] 85 × [latex]\frac{375}{17}[/latex] = ? 5 × 375 = ? ? = 1875
5. What should come at the place of Question mark (?) in the following question? 2[latex]\frac{11}{13}[/latex] - 3[latex]\frac{1}{13}[/latex] + 5[latex]\frac{1}{4}[/latex] = ? × 87

A. [latex]\frac{4}{15}[/latex] B. [latex]\frac{6}{13}[/latex] C. [latex]\frac{3}{52}[/latex] D. [latex]\frac{21}{52}[/latex]

Answer: Option C
Explanation:2[latex]\frac{11}{13}[/latex] - 3[latex]\frac{1}{13}[/latex] + 5[latex]\frac{1}{4}[/latex] = ? × 87 (2 – 3 + 5) + [latex]\frac{11}{13}[/latex] - [latex]\frac{1}{13}[/latex] + [latex]\frac{1}{4}[/latex] = ? x 87 4 + [latex]\frac{44 – 4 + 13 }{52}[/latex] = ? × 87 4 + [latex]\frac{53}{52}[/latex] = ? × 87 [latex]\frac{261}{52}[/latex] = ? × 87 [latex]\frac{261}{52 × 87}[/latex] = ? ? = [latex]\frac{3}{52 }[/latex]

Directions(1-5): Number Series 1. 24, 12, 12, 18, ? , 90

A. 40 B. 38 C. 36 D. 45

Answer: Option C
Explanation:
2. 13, 19, 30, 48, 75, ?

A. 107 B. 108 C. 116 D. 113

Answer: Option D
Explanation:
3. 2, 8, 26, ?, 242

A. 78 B. 72 C. 82 D. 80

Answer: Option D
Explanation:
4. 7, 13, ?, 49, 97

A. 27 B. 25 C. 23 D. 29

Answer: Option B
Explanation:
5. 5, 16, 49, 104, ?, 280

A. 165 B. 160 C. 171 D. 181

Answer: Option D
Explanation:

Directions(1-5): Time and Work 1. A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the same work, If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is:

A. 100 B. 96 C. 95 D. 90

Answer: Option B
Explanation: Let 1 day's efficiency of each of the individuals is A, B and C respectively. As per the given information, we get the efficiency equations as follows 3A = (B + C) ...(i) A + B + C = 24 .....(ii) Putting 3A in place of (B + C) in equation (ii), we get A + 3A = 24 4A = 24 Now, 4A do the whole work in 24 days. Therefore, A alone will do the whole work in 24 × 4 = 96 days
2. 4 boys and 3 women can do a piece of work in 6 days while 2 boys and 4 women can do the same piece of work in 9 days. How much time will be taken by 7 boys and 9 women to do the same piece of work?

A. 3 days B. 7 days C. 8 days D. 12 days

Answer: Option A
Explanation: As per the given information, work done by 4 boys and 3 women in 6 days must be equal to work done by 2 boys and 4 women in 9 days. Therefore, we get (4B + 3W) × 6 = (2B + 4W) × 9 ⇒ 24B + 18W = 18B + 36W ⇒ 6B = 18W ⇒ 1B = 3W Now, 2B + 4W= (2 × 3)W + 4W = 10W ⇒ 10 women do a piece of work in 9 days. Similarly, 7B + 9W = (7 × 3)w + 9W = 30W Now, when 10 women do a piece of work in 9 days, 30 women (thrice of 10) will do the same piece of work in 3 days (∵ Time ∝ 1/Efficiency ).
3. Working alone, Typewriters A, B, C can do a certain typing job, consisting of a large number of pages, in 12, 15 and 18 hours, respectively. What is the ratio of the time it takes Typewriter A to do the job, working alone at its rate, to the time it takes Type writer B and C to do the job, working together at their individual rate?

A. [latex]\frac{4}{11}[/latex] B. [latex]\frac{1}{2}[/latex] C. [latex]\frac{15}{22}[/latex] D. [latex]\frac{22}{15}[/latex]

Answer: Option D
Explanation: Since Typewriter B can do the job in 15 hours, it can do [latex]\frac{1}{15}[/latex] of the job in 1 hour. Since Typewriter C can do the job in 18 hours it can do [latex]\frac{1}{18}[/latex] of the job in 1 hour. Together Typewriters B and C can do = ([latex]\frac{1}{15}[/latex] + [latex]\frac{1}{18}[/latex]) = [latex]\frac{6}{90}[/latex] + [latex]\frac{5}{90}[/latex] = [latex]\frac{11}{90}[/latex] of the job in 1 hour Which means that it takes them = [latex]\frac{11}{90}[/latex] hours to complete the job. Since Typewriter A completes the job in 12 hours, the ratio of the time required for A to do the job to the time required for B and C working together to do the job is [latex]\frac{12}{\frac{90}{11}}[/latex] = [latex]\frac{12(90)}{11}[/latex] = [latex]\frac{2(11)}{15}[/latex] = [latex]\frac{22}{15}[/latex]
4. A, B and C can do a piece of work in 4, 7 and 8 days respectively. They undertook to finish the work together for Rs. 53650. Find the difference (in Rs.) between the share of A and that of B

A. 10100 B. 11100 C. 11650 D. 12560

Answer: Option B
Explanation: The ratio of shares of A, B and C = The [latex]\frac{1}{4}[/latex]:[latex]\frac{1}{7}[/latex]: [latex]\frac{1}{8}[/latex] = [latex]\frac{14}{56}[/latex]:[latex]\frac{8}{56}[/latex]: [latex]\frac{7}{56}[/latex]= 14 : 8 : 7 Difference between the shares of A and B in ratio = [latex]\frac{6}{29}[/latex] ∴ Actual difference in value = [latex]\frac{6}{29}[/latex]× 53650 = 11,100/-
5. P is thrice as good a workman as Q and together they finish a piece of work in 24 days. The number of days taken by P alone to finish the work is:

A. 25 days B. 22 days C. 32 days D. 34 days

Answer: Option C
Explanation: P's 1 days' work) : (Q's 1 days' work) = 3 : 1 (P + Q)'s = 1 days work = [latex]\frac{1}{24}[/latex] Divide [latex]\frac{1}{24}[/latex] in the ratio 3 : 1 P's 1 day's work = [[latex]\frac{1}{24}[/latex] x [latex]\frac{3}{4}[/latex]]⇒ [latex]\frac{1}{32}[/latex] Hence, P alone can finish the work in 32 days.