Aptitude Questions – 2 (for CAT and Bank Exams)
1. If a-3 = b3/2 and b = 4 then ‘a’ can take which of the following values?
(a) ½ (b) -1/8 (c) ¼ (d) 1/8 (e) 2
a-3 = b3/2 = 43/2 = 23. Thus a-3 = 23 -> a-1 = 2 -> a = ½.
Hence a = ½.
2. An empty basket, with a capacity for 50 oranges costs Rs 7.25. For the first 15 oranges bought each orange costs Rs 0.75 and every extra orange bought costs Rs 0.50 each. If a man has Rs 31.00 with him, what is the maximum number of oranges along with the requisite number of baskets for putting them in, he can buy?
(a) 31 (b) 62 (c) 40 (d) 50 (e) 47.
Let ‘n’ be the number of oranges that he bought along with one basket.
(option (b) alone requires more than one basket and it does not fit into the information given)
Now we have an equation —– 7.25 + (15 x 0.75) + (n – 15) x 0.50 = 31.00 (all figures in rupees)
7.25 + 11.25 + (n-15)x0.50 = 31.00 -> (n-15)x0.50 = 31.00 – 18.50 -> 12.50.
Thus (n-15) = 25 -> n = 25 + 15 = 40.
3. In a certain party, the ratio of boys to girls was 5 : 3 initially. After some time 10 boys left the party and the ration now became 1 : 1. How many people were originally there at the party?
(a) 48 (b) 32 (c) 64 (d) 40 (e) 56
No working required and the question can be answered from the choices.
4. If x3 = -27 and if y3 = (x2 + 7)(x – 1) then which of the following value ‘y’ can take?
(a) 2 x 3√4 (b) -2 (c) -4 (d) 2 (e) none of these
X3 = -27. Hence ‘x’ = -3. Y3 = (x2 + 7)(x – 1) -> (9 + 7)(-3-1) -> 16 x (-4) = -64. (after substituting
The value of ‘x’)
Thus ‘y3 = -64 and ‘y’ = -4.
5. a/4 + 4/a + a/4 + 4/a + a/4 + 4/a —————–
In the above sequence the odd numbered term is a/4 and the even numbered term is 4/a.
What is the sum of the first 40 terms of the sequence?
(a) 80 + 5a2 (b) (80 + 5a)/a (c) (80 + 5a2)/a (d) (80 + a2)/a (e) (5 + a)/80
Sum of 20 odd terms —— a/4 x 20 = 20a/4 -> 5a………… (i)
Sum of 20 even terms——4/a x 20 = 80/a…………………… (ii)
The sum of 40 terms in the sequence is — (i) + (ii) ——— 5a + 80/a -> (5a2 + 80)/a
6. A and B together worked for 4 hours and completed ½ of the job. A worked thrice as fast as B did. B left and A was joined by C and they finished the remaining job in 1 hour. How long C would have taken to complete the whole job by himself?
(a) 3 hours (b) 7/2 hours (c) 32/13 hours (d) 4 hours (e) 16/5 hours
Let ‘x’ be the time taken by A to complete the job while B takes 3x time to complete.
In 4 hours A & B together would have done —- 4/x + 4/3x = 16/3x job.
In four hours they have done 16/3x job that is equal to ½. -> 3x = 32 and x = 32/3
Let C take ‘c’ hours to complete the job.
In one hour A and C together finished the remaining job.
ie 1/x + 1/c = ½ -> 1/(32/3) + 1/c = ½ -> 3/32 + 1/c = ½
1/c = ½ – 3/32 = 13/32
Hence C will take 32/13 hours to complete the job.
7. In a party there are 12 boys and 15 girls. In how many different dancing pairs can be made out of the group?
(a) 60 (b) 180 (c) 150 (d) 300 (e) 250
The dancing pairs are —– 12C1 x 15C1 -> 12 x 15 = 180
8. A family consists of father, mother, son and daughter. The father is five years elder to his wife. The daughter is 23 years younger to her father and the son is 16 years younger to his mother. What is the difference in age between the son and the daughter?
(a) 17 years (b) 7 years (c) 5 years (d) 2 years (e) None of these
Let F, M, S and D be the ages of the father, mother, son and daughter.
F = M + 5. D = M + 5 – 23 ( F – 23 ) = M – 18.
S = M – 16
D = M – 18. Hence the difference between B and D is 2.
9. A shopkeeper marks the price of an item 60% over its cost price. However, during a sale promotion period he offered a discount of 40% on the marked price. If a customer pays Rs 24.00 for the item what is the profit/loss in the transaction for the trader?
(a) Rs 4 profit (b) Rs 2 profit (c) Rs 16 loss (d) Re 1 loss (e) Rs 4 loss
Let the cost price be ‘x’. Then the marked price is —- 1.6x (60% up)
On 1.6x the discount allowed is 0.64x (40% discount on the marked price)
Thus the realized value of the item is —- 0.96x and this equals to Rs 24 (the amount customer paid)
Hence the cost price of the item is x = 24 x 100/0.96 = Rs 25.
CP = 25. SP = 24. Hence the loss is Re 1 in the transaction.
10. A tank of volume 432 cu.ft.has one inlet and two outlet pipes. The inlet pipe fill the tank at the rate of 4 cu.in per minute, while the two outlet pipes drain the tank at the rate of 14 cu. In and 6 cu. In per minute respectively. If all the three pipes are opened when the tank is full, in how much time the tank will become empty?
(a) 777.6 hrs (b) 3 days (c) 15 days (d) 77.76 hrs (e) None of these.
This is a tricky question. Please note the volume of the tank is given in cubic feet while the inlet pipes filling and draining is given in cubic inches per minute. Hence the first thing to do is to convert the volume into cubic inches.
Volume of the tank — 432 cu.ft -> 432 x 12 x 12 x 12 = 746496 cubic inches ( 12 inches make one foot)
In one minute when the three pipes are opened the effective reduction in the volume is
—– 4 – 14 – 6 = -16 (When the tank is full in each minute the volume gets reduced by 16 cubic inches.
Hence, to drain 746496 cubic inches it would take — 746496/16 = 46656 minutes or
46656/60 = 777.6 hours.