**The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is**- 0
- 1
- 2
- 3

Answer: Option C.

Let the numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

=> xy = 77

∴ Possible pairs = (1,77) and (7,11)

**What is the least number which, when divided by 5, 6, 7, 8 gives the remainder 3 but is divisible by 9?**- 1463
- 1573
- 1683
- 1793

Answer: Option C.

LCM of 5, 6, 7, 8 = 35 × 24 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9.

For k = 2, it is divisible by 9.

∴ Required number = 840k + 3

= 840 × 2 + 3 = 1683**Three numbers are in the ratio 3:4: 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is**- 20
- 27
- 39
- 52

Answer: Option C.

Let the numbers be 3x, 4x and 5x.

∴ 5x + 3x = 4x + 52

=> 4x = 52 => x =13

∴ The smallest number = 3x = 3 × 13 = 39**If the radius of a circle is in creased by 50%, its area is increased by**- 125%
- 100%
- 75%
- 50%

Answer: Option A.

Percentage increase in area

**A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in**- 10 2/3 days
- 10 1/2 days
- 10 1/4 days
- 10 1/3 days

Answer: Option C.

Part of work done by A and B in first two days

Part of work done in first 10 days = 35/36

Remaining work = 1 – 35/36 = 1/36

Now it is the turn of A.

∴ Time taken by A = 1/36 × 9 = ¼

∴ Total time = 10 + ¼ = 10 ¼ daysDE Shaw Preparation Links- Sample Aptitude Questions of DE Shaw
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**In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?**- 12 years
- 11 years
- 10.5 years
- 10 years

Answer: Option B.

Father + mother = 2 × 35 = 70 years

Father + mother + son = 27 × 3 = 81 years

Son’s age = 81 – 70 = 11 years**If 5 men or 7 women can earn Rs. 5,250 per day, how much would 7 men and 13 women earn per day?**- Rs. 11,600
- Rs. 11.700
- Rs. 16,100
- Rs. 17,100

Answer: Option D.

5 men = 7 women

7 men

Mark Price = 140

7 men + 13 women

Now,

∵ 7 women = Rs. 5250

**If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?**- 60
- 45
- 40
- 30

Answer: Option A.

(A + B)’s 1 day’s work =

B’s 1 day’s work =

A’s 1 day’s work =

A alone will do the work in 60 days.**By walking at 3/4 of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is**- 75 minutes
- 60 minutes
- 40 minutes
- 30 minutes

Answer: Option B.

of usual time = Usual time + 20 minutes

of usual time

= 20 minutes

Usual time = 20 × 3 = 60 minutes**4.41*0.16/2.1*1.6* 0.21 is simplified to**- 1
- 0.1
- 0.01
- 10

Answer: Option A.