Direction: Find out the wrong number in the series. 1. 7, 8, 18, 57, 228, 1165, 6996

8 B. 18 C. 57 D. 228

Answer: Option D
Explanation: Let the given numbers be A, B, C, D, E, F, G. Then, A, A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required numbers. Clearly, 228 is wrong.
2. 1, 1, 2, 6, 24, 96, 720

A. 720 B. 96 C. 24 D. 6

Answer: Option B
Explanation: Go on multiplying with 1, 2, 3, 4, 5, 6 to get next number. So, 96 is wrong.
3. 64, 71, 80, 91, 104, 119, 135, 155

A. 71 B. 80 C. 104 D. 135

Answer: Option D
Explanation: Go on adding 7, 9, 11, 13, 15, 17, 19 respectively to obtain the next number. So, 135 is wrong.
4. 15, 16, 34, 105, 424, 2124, 12756

A. 16 B. 34 C. 105 D. 2124

Answer: Option D
Explanation: [latex]{2}^{nd}[/latex] term = [latex]{1}^{st}[/latex] x 1 + 1 = 15 x 1 + 1 = 16 [latex]{3}^{rd}[/latex] term = [latex]{2}^{nd}[/latex] x 2 + 2 = 16 x 2 + 2 = 34 [latex]{4}^{th}[/latex] term = [latex]{3}^{rd}[/latex] x 3 + 3 = 34 x 3 + 3 = 105 [latex]{5}^{th}[/latex] term = [latex]{4}^{th}[/latex] x 4 + 4 = 105 x 4 + 4 = 424 [latex]{6}^{th}[/latex] term = [latex]{5}^{th}[/latex] x 5 + 5 = 424 x 5 + 5 = 2125 [latex]{6}^{th}[/latex] term should 2125 instead of 2124
5. 10, 26, 74, 218, 654, 1946, 5834

A. 26 B. 74 C. 218 D. 654

Answer: Option D
Explanation: [latex]{2}^{nd}[/latex] term = [latex]{1}^{st}[/latex] x 3 - 4 = 10 x 3 - 4 = 26 [latex]{3}^{rd}[/latex] term = [latex]{2}^{nd}[/latex] x 3 - 4 = 26 x 3 - 4 = 74 [latex]{4}^{th}[/latex] term = [latex]{3}^{rd}[/latex] x 3 - 4 = 74 x 3 - 4 = 218. [latex]{5}^{th}[/latex] term = [latex]{4}^{th}[/latex] x 3 - 4 = 218 x 3 - 4 = 650. [latex]{5}^{th}[/latex] term must be 650 instead of 654

1. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

A. 123 B. 127 C. 235 D. 305

Answer: Option B
Explanation: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032 = 127.
2. Which of the following has the most number of divisors?

A. 99 B. 101 C. 176 D. 182

Answer: Option C
Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors.
3. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then some of the number is:

A. 28 B. 32 C. 40 D. 64

Answer: Option C
Explanation: Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 48 or x = 8. The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40.
4. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

A. 15 cm B. 25 cm C. 35 cm D. 42 cm

Answer: Option C
Explanation: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
5. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

A. 504 B. 536 C. 544 D. 548

Answer: Option D
Explanation: Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

1. A began a business with Rs. 85,000. He was joined afterward by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3: 1?

A. 4 months B. 5 months C. 6 months D. 8 months

Answer: Option D
Explanation: Suppose B joined for x months. Then, Then, [latex]\frac{85000 × 12}{42500 × x }[/latex] = [latex]\frac{3}{1 }[/latex] x = [latex]\frac{85000 × 12}{42500 × 3 }[/latex] = 8
2. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?

A. 7: 6: 10 B. 12: 15: 16 C. 42: 45: 56 D. Cannot be determined

Answer: Option B
Explanation: Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.
3. Arun, Kamal, and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?

A. Rs. 890 B. Rs. 1335 C. Rs. 1602 D. Rs. 1780

Answer: Option A
Explanation: Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8) = 48 : 32 : 64 = 3 : 2 : 4. Kamal's share = Rs. 4005 X [latex]\frac{2}{9 }[/latex] = Rs. 890.
4. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?

A. Rs. 9,423 B. Rs. 10,250 C. Rs. 12,500 D. Rs. 10,500

Answer: Option D
Explanation: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4. Simran's share = Rs. 24500 x [latex]\frac{3}{7 }[/latex]
5. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

A. 3 : 5 : 2 B. 3 : 5 : 5 C. 6 : 10 : 5 D. Data inadequate

Answer: Option C
Explanation: Let the initial investments of A and B be 3x and 5x. A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.