5. J can dig a well in 16 days. P can dig a well in 24 days. J, P, H dig in 8 days. H alone can dig the well in How many days?

a) 32

b) 48

c) 96

d) 24

Assume the total work = 48 units.

Capacity fo J = 48 / 16 = 3 units / day

Capacity of P = 48 / 24 = 2 units / day

Capacity of J, P, H = 48 / 8 = 6 units / day

From the above capacity of H = 6 – 2 – 3 = 1

So H takes 48 / 1 days = 48 days to dig the well

6. If a lemon and apple together costs Rs.12, tomato and a lemon cost Rs.4 and an apple costs Rs.8 more than a lemon. What is the cost of lemon?

L + A = 12 …(1)

T + L = 4 …..(2)

L + 8 = A

Taking 1 and 3, we get A = 10 and L = 2

7. 3 mangoes and 4 apples costs Rs.85. 5 apples and 6 peaches costs 122. 6 mangoes and 2 peaches costs Rs.144. What is the combined price of 1 apple, 1 peach, and 1 mango.

a) 37

b) 39

c) 35

d) 36

Sol: Note: It is 114 not 144.

3m + 4a = 85 ..(1)

5a + 6p = 122 ..(2)

6m + 2p = 114 ..(3)

(1) x 2 => 6m + 8a = 170

(3) => 6m + 2p = 114

Solving we get 8a – 2p = 56 ..(4)

(2) => 5a + 6p = 122

3 x (4) = 24a – 6p = 168

Solving we get a = 10, p = 12, m = 15

So a + p + m = 37

8. An organisation has 3 committees, only 2 persons are members of all 3 committee but every pair of committee has 3 members in common. what is the least possible number of members on any one committee?

a) 4

b) 5

c) 6

d) 1

Sol:

Total 4 members minimum required to serve only on one committee.

9. There are 5 sweets – Jammun, kaju, Peda, Ladu, Jilebi which can be consumed in 5 consecutive days. Monday to Friday. A person eats one sweet a day, based on the following constraints.

(i) Ladu not eaten on monday

(ii) If Jamun is eaten on Monday, Ladu should be eaten on friday.

(iii) Peda is eaten the day following the day of eating Jilebi

(iv) If Ladu eaten on tuesday, kaju should be eaten on monday

based on above, peda can be eaten on any day except

a) tuesday

b) monday

c) wednesday

d) friday

From the (iii) clue, peda must be eaten after jilebi. so Peda should not be eaten on monday.

10. If YWVSQ is 25 – 23 – 21 – 19 – 17, Then MKIGF

a) 13 – 11 – 8 – 7 – 6

b) 1 – 2-3-5-7

c) 9 – 8 – 7 – 6 – 5

d) 7 – 8 – 5 – 3

MKIGF = 13 – 11 – 9 – 7 – 6

Note: this is a dummy question. Dont answer these questions

11. Addition of 641 + 852 + 973 = 2456 is incorrect. What is the largest digit that can be changed to make the addition correct?

a) 5

b) 6

c) 4

d) 7

Sol:

641

852

9**6**3

——

2466

Largest among tens place is 7, so 7 should be replaced by 6 to get 2456

12. Value of a scooter depriciates in such a way that its value at the end of each year is 3/4th of its value at the beginning of the same year. If the initial value of scooter is 40,000, what is the value of the scooter at the end of 3 years.

a) 23125

b) 19000

c) 13435

d) 16875

value of the scooter at the end of the year = 40000×(34)340000×(34)3 = 16875

13. At the end of 1994, R was half as old as his grandmother. The sum of the years in which they were born is 3844. How old R was at the end of 1999

a) 48

b) 55

c) 49

d) 53

In 1994, Assume the ages of GM and R = 2k, k

then their birth years are 1994 – 2k, 1994 – k.

But given that sum of these years is 3844.

So 1994 – 2k + 1994 – k = 3844

K = 48

In 1999, the age of R is 48 + 5 = 53

14. When numbers are written in base b, we have 12 x 25 = 333, the value of b is?

a) 8

b) 6

c) None

d) 7

Let the base = b

So, (b+2)(2b+5) = (b+2)(2b+5)=3b2+3b+3(b+2)(2b+5)=3b2+3b+3

2b2+9b+10=3b2+3b+32b2+9b+10=3b2+3b+3

b2−6b−7=0b2−6b−7=0

Solving we get b = 7 or -1

So b = 7

15. How many polynomials of degree >=1 satisfy f(x2)=[f(x)]2=f(f(x)f(x2)=[f(x)]2=f(f(x)

a) more than 2

b) 2

c) 0

d) 1

Sol:Let f(x) = x2x2

f(x2)=[x2]2=x4f(x2)=[x2]2=x4

(f(x))2=[x2]2=x4(f(x))2=[x2]2=x4

f(f(x))=f(x2)=[x2]2=x4f(f(x))=f(x2)=[x2]2=x4

Only 1

16. Figure shows an equilateral triangle of side of length 5 which is divided into several unit triangles. A valid path is a path from the triangle in the top row to the middle triangle in the bottom row such that the adjacent triangles in our path share a common edge and the path never travels up (from a lower row to a higher row) or revisits a triangle. An example is given below. How many such valid paths are there?

a) 120

b) 16

c) 23

d) 24

Sol:

Number of valid paths = (n-1) ! = (5-1)! = 24

17. In the question, A^B means, A raised to power B. If x*y^2*z < 0, then which one of the following statements must be true?

(i) xz < 0 (ii) z < 0 (iii) xyz < 0

a) (i) and (iii)

b) (iii) only

c) None

d) (i) only

As y^2 is always positive, x*y^2*z < 0 is possible only when xz < 0. Option d is correct.

18. The marked price of a coat was 40% less than the suggested retail price. Eesha purchased the coat for half the marked price at the fiftieth anniversary sale. What percentage less than the suggested retail price did Eesha pay?

a) 60

b) 20

c) 70

d) 30

Let the retail price is Rs.100. then market price is (100-40) % of 100 = 60. Eesha purchased the coat for half of this price. ie., 30 only. which is 70 less than the retail price. So Option C is correct.