FCI General Intelligence and aptitude

FCI Assisstatn Grade III questions with answers for practice 

FCI Arithmetical Ability

1.   The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is –  

a.   74

b.   78

c.   80

d.   90

Ans : Let the numbers be x and y .

∴  xy = 1575

And  x/y = 9/7

∴  xy/x/y = 1575/9/7

∴   y2  = 1225

∴ y = 35 and x = 45

∴  The sum of the numbers = 45+35

  = 80

2.   The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __

 a.   3

b.   6

c.   9

d.   8.2

Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)

= 314.4+5.4-16.8-1

= 32

= 9

3.   √6+√6+√6+… is equal to –

a.   2

b.   5

c.   4

d.   3

Ans : Let √6+√6+√6+…. be x.

∴   x =√6+x

∴   x2 = 6+x

∴   x2 + x – 6 = 0

∴   (x-3) (x+2) = 0

∴   x = 3

4.   The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is –

a.   24

b.   32

c.   40

d.   28

Ans : Let the consecutive odd numbers be x and (x+2)

∵ x2 + (x + 2)2 = 394

∴  x2 + x2 + 4x + 4 = 394

∴  2 x2 +4x – 390 = 0

∴  x2 + 2x – 195 = 0

∴ (x +15) (x-13) = 0

∴  x = 13

∴   Required sum = 13 +15 =28

5.   When (6767 +67) is divided by 68, the remainder is-

a.   1

b.   63

c.   66

d.   67

Ans:  (6767+ 67) = 67(6766 + 166)

As 66 is an even number

∴  6766 is an even number

∴  (6766 + 1) is perfectly divisible by (67 + 1)

i.e. 68

∴  The remainder = 67

6.   In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend then-

a.   4b-a2 /a  =3

b.   4b-2a /a2 =2

c.   (a+1)2 = 4b

d.   A(a+2)/b = 4

Ans : As  divisor is a, and dividend is b.

∴   Quotient = a/4

And Remainder = a/2

∴   b = a * a/4 + a/2

∴   4b = a2 + 2a

∴   a(a+2)/b = 4

7.   If 738 A6A is divisible by 11, then the value of A is-

a.   6

b.   3

c.   9

d.   1

Ans :  As 738A6 A is divisible by 11.

∴   A + A + 3 = 6 + 8 + 7

∴   A = 9

8.   The east positive integer that should be subtracted from 3011 * 3012 so that the difference is perfect square is-

a.   3009

b.   3010

c.   3011

d.   3012

Ans :  ∵ 3011 * 3012 = 3011 (3011 + 1)

= (3011)2 + 3011

∴   Required least number = 3011

9.   P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-

a.   2850

b.   3750

c.   2750

d.   1000

Ans :  Work done by Q = 19/23 + 8/23 – 1

4/23

∴  Wage of Q = 4/23 * 5750

= Rs. 1000

10.  A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin  to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?

a.   15

b.   20

c.   18

d.   30

Ans :  Work done by A = 6/24 = ¼

Work done by B = (x-6)/32

(where x is no. of days in which work is competed)

 

∵  ¼ + x – 6/32 + x/64 = 1

∴  16 + 24 – 12 + x /64 = 1

∴  3x + 4 = 64

∴  x = 60/3 = 20 days

11.  The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-

a.   1

b.   2

c.   3

d.   4

Ans :  The square root of

[(0.75)3/1 – 0.75 + {0.75 + (0.75)2 + 1}]

= √1.6875 + 2.3125

=√4

= 2

12.  Given that √4096 = 64, the value of √4096 + √40.96 +√0.004096 is-

a.   70.4

b.   70.464

c.   71.104

d.   71.4

Ans : Given Exp. = √4096 + √40.96 +√0.004096

= 64 + 6.4 + 0.064

= 70.464

13.  By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is-

a.   5 : 3

b.   3 : 5

c.   3 : 4

d.   4 : 3

Ans :  Let of M.P. be Rs. x.

∴ S.P. = Rs.3x/4

and C.P. = 3x/4 * 100/125

= Rs.3x/5

∴ required ratio = x: 3x/5

= 5:3

14.  A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, the monthly income of B is-

a.   Rs.7,000

b.   Rs.14,000

c.   Rs.5,000

d.   Rs.10,000

Ans :  Let the monthly income of B be Rs. x.

∴  Monthly income of A = Rs. 2x and

Saving of A =5000 * 4/(4 + 1)

= Rs. 4000

Saving of B = Rs.1000

∵ 2x – 4000/x-1000 = 5/3

⇒  6x – 12000 = 5x – 5000

∴  x = Rs.7000

15.  The ratio of the sum of two numbers and their difference is 5:1. The ratio of the greater number to the smaller number is-

a.   2 : 3

b.   3 : 2

c.   5 : 1

d.   1 : 5

Ans : Let the numbers be x and y.

∵ x + y/ x – y = 5/1

⇒  5x – 5y = x + y

⇒  4x = 6y

⇒  x/y = 6/4

x : y = 3 : 2

16.  A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at-

a.   7.12 p.m.

b.   7.15 p.m.

c.   7.10 p.m.

d.   7.18 p.m.

Ans : Let the cistern be emptied at x p.m.

∵ x -3/3 + x – 4/4 = x - 5/1

&r