Aptitude Questions – 2 (for CAT and Bank Exams)

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
Ans: (a)
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.
Ans: (c)
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
Ans: (d)
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
Ans: (c)
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
Ans: (c)
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
Ans: (c)
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
Ans: (b)
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
Ans: (d)
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
Ans: (d)
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.
Ans: (a)
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.

Aptitude Questions (for CAT and Bank Exams)

Aptitude Questions ( for CAT and Bank exams)

1. A regular working day is of 8 hours and a regular week is 5 working days. A worker is paid Rs 24 per regular hour and Rs 32 per hour over time. If the worker earns Rs 4320.00 in four weeks then what is the total number of hours he worked?
(a) 180 (b) 175 (c) 160 (d) 195 (e) 200
Ans: (b)
During the four weeks the worker would have worked normal hours of — 5 x 8 x 4 = 160 hours.
For this normal working of 160 hours his wages will be —– 24 x 160 = Rs 3840.00
He actually earned Rs 4320 during the four weeks of working.
Thus the difference amount — Rs 4320 – Rs 3840 = Rs 480 represents his overtime.
His overtime wages for one hour is Rs 32 and hence he had worked overtime
For —— 480 / 32 = 15 hours.
Thus totally in 4 weeks he worked ——- 160 + 15 = 175 hours.

2. Five apples and four oranges cost the same as three apples and seven oranges. What is the ratio of the following —– cost of one orange / cost of one apple ?
(a) 2 : 3 (b) 3 : 4 (c) 3 : 1 (d) 4 : 3 (e) 2 : 5
Ans: (a)
5 A + 4 O = 3 A + 7 O -> 2 A = 3 O -> O/A = 2/3 Ratio O : A = 2 : 3

3. The average of 2, 7, 6, and X is 5.The average of 18, 1, 6, X, and Y is 10. What is the value of ‘Y’?
(a) 20 (b) 30 (c) 10 (d) 5 (e) 15
Ans: (a)
The total of —- 2 + 7 + 6 + x = 5 * 4 = 20. Hence the value of x = 20 – 15 = 5
The total of —- 18 + 1 + 6 + x + y = 10 * 5 = 50. Now substituting the value of x in this we get
— 18 + 1 + 6 + 5 + y = 50.
Hence y = 50 – 30 = 20.

4. In a certain boy’s camp, 20% of boys are from Maharashtra State and 30% of those are from Mumbai city. If there are 49 boys in the camp who are from Maharashtra State but not from Mumbai city, then what is the total number of boys in the camp?
(a) 70 (b) 245 (c) 163 (d) 350 (e) 817
Ans: (d)
Boys from Maharashtra State in the camp are 20%.
Of this, Boys from Mumbai city is 30% of 20% -> 6%
Excluding Mumbai city boys from Maharashtra State is —- 20% – 6% = 14% this is equal to 49 boys.
Hence the total number of boys in the camp is —- (49 x 100) / 14 = 350 boys.

5. The sum of the quotient and the reminder obtained when a number is divided by 4 is 8 and the sum of their squares is 34. Which of the following is the number?
(a) 17 (b) 26 (c) 21 (d) 23 (e) 29
Ans: (d)
23 when divided by 4 will give a quotient 5 and reminder 3. Sum of these aggregates to 8
The square of 5 is 25 and the square of 3 is 9. Aggregate of these two amounts to 34.

6. If the average of ‘m’ numbers is ‘a’ and when ‘x’ is added to the ‘m’ numbers the average of (m+1) numbers is ‘b’. then ‘x’ is equal to which of the following?
(a) Ma+b (b) m(a+b) (c) 2ma – mb (d) b-a+ma (e) (m+1)b – ma.
Ans: (e)
(ma + x) / m + 1 = b -> ma + x = mb + b -> x = mb + b – ma -> m(b – a) + b -> (m + 1)b – ma

7. If the ratio of A to B and ratio of X to Y are both equal to 1/3, then the ratio of (A + X) to (B + Y) is equal to:
(a) 5/6 (b) 1/12 (c) 1/3 (d) ½ (e) 1/6
Ans: (c)
A/B = X/Y = I/3 —– (A+X) / (B+Y) = ? Please observe the following:
2/4 = 3/6 = ½ —– (2+3) / (4+6) = 5/10 = ½.

8. P, Q and R, are all multiples of 5. Q is greater than P and less than R and R is greater than P. What is the value of (P-Q)(P-R) / (Q-R)
(a) -10 (b) -5 (c) 1 (d) 10 (e) cannot be determined
Ans: (a)
Let the values of P, Q and R be respectively 5, 10 and 15.
Then we have —- (5 – 10)(5-15) / (10-15) —— solving we get the answer — (-10)

9. Twice some value of ‘a’ is greater than another value ‘b’. But, twice ‘b’ is greater than twice ‘a’. If ‘c’ is less than one half of “b’ hen which of the following is correct?
(a) c < a < b (b) c > b > a (c) a < c < b (d) a < 2 < c < b/2 (e) c > a > b
Ans: (a)
Let us apportion value 4 for ‘a’. then, 2a = 8
Let the value of ‘b’ be 6. Then 2a is greater than ‘b’. But, 2b = 12 is greater than 2a.
Half of ‘b’ is ‘c’ and this equals to 3.
Hence we find, c (3) < a (4) < b (6) 10. A company manufactures two products A and B. Product A requires 3 units of material 1 and 4 units of material 2 for producing one unit of A. Product B requires 5 units of material 1 and 7 units of material 2 for producing one unit of B. If 26 units of A and B were produced, how many units of material 2 were used in the process? (a) 213 (b) 293 (c) 384 (d) 286 (e) None of these. Ans: (d) A simple question. Totally 4 + 7 = 11 units of material 2 is required in the process of producing one unit of A and B. Hence, for producing 26 units of each A and B the total quantity of material 2 required is ----- 26 x 11 = 286 units.