**AMCAT**

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### All questions are Multiple-Choice-Questions with only one optionas the correct answer.

Q1. In a kilometre race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?

a. 150 s

b. 450 s

c. 750 s

d. 825 s

ans:c

Q2. Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill another tank twice as big as the first. If A has a cross sectional circumference that is one-third of C, how long will it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross-sectional area is same for all the three pipes.)

a. 66/13

b. 40/13

c. 16/13

d. 32/13

ans:d

Q3. Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number.

a. 6

b. 18

c. 12

d. All of these

ans:d

Q4. The arithmetic mean of 2 numbers is 34 and their geometric mean is 16. One of the numbers will be

a. 4

b. 16

c. 18

d. 12

ans:a

Q5. If x% of a is the same as y% of b, then z% of b is :

a. (xy/z)% of a

b. (yz/x)% of a

c. (xz/y)% of a

d. None of these

ans:c

Q6. The letters of the word WOMAN are written in all possible orders and these words are written out as in a dictionary ,then the rank of the word ‘WOMAN’ is

a. 117

b. 120

c. 118

d. 119

ans:c

Q7. What least number must be subtracted from 9400 to get a number exactly divisible by 65?

a. 40

b. 20

c. 80

d. none of these

ans:a

Q8. If 2505 / 0.5 = 5010 then 25.05 / 0.5 = ?

a. 5.010

b. 50.10

c. 501.0

d. None of these

ans:b

Q9. Which pair of rational numbers lie between 1/5 and 2/5 –

a. 262/1000, 275/1000

b. 362/1000, 562/1000

c. 451/1000, 552/1000

d. 121/1000,131/1000

ans:q

Q10. What is the value of the following expression: 2 log10 5 + log10 4 ?

a. 2

b. 2.5

c. 3

d. None of these

ans:2

Q11. If x increases linearly, how will a-x behave (a>1) ?

a. Increase linearly

b. Decrease linearly

c. Increase exponentially

d. Decrease exponentially

Q12. What is the probability of getting the sum 5 in two throws of the dice?

a. 1/12

b. 1/5

c. 1/9

d. None of these

#### Solutions:

1) let speed of A = x m/s & speed of B = y m/s then

1000/x +19 = (1000-40)/y => 1000/x = 960/y -19 —-(1)

(1000-30*y)/y = (1000 -40)/x => 960/x = 1000/y -30 —-(2)

dividing (1) by (2)

=> 1000/960 = (960 – 19y) / (1000 – 30y)

=> 25(1000 -30y) = 24(960 -19y)

=> y = 20/3 m/s

so, x = 8 m/s

time taken by B to run 5000 m

= 5000/y

= 5000/(20/3)

= 5000*3/20

= 750 sec

(c)

2) let circumferences of A be x then its area is proportional to x^2

A = x , x^2

C = 3x, 9x^2

B = (2/3)*3x = 2x, 4x^2

pipe A x^2, in 16 min

pipe(B+C) 13x^2, in 16/13 min

second tank = 2*16/13 = 32/13 min

(d)

3) let three consecutive whole numbers are (x-1),x,(x+1)

given, x^2 greater than (x-1)*(x+1)+1=x^2-1+1=x^2

its true for all x

(d)

4) x+y=2*34 =68

& (x*y)^(1/2)=16 => xy=256 =>x*(68-x)=64*4 => x=4,64

(a)

5) x% of a = y% of b => x*a/100 =y*b/100 => ax=by => b=a*(x/y)

then z% of b = z% of a*(x/y)=(zx/y)*(a/100) = (xz/y)% of a

(c)

6) No. of words starting with A => 4!

M => 4!

N => 4!

O => 4!

WA => 3!

WM => 3!

WN => 3!

WO => 3!

WOA => 2!

next is WOMAN

rank of WOMAN = 4*(4!) + 3*(3!)+ 2! + 1 = 117

(a)

7) 9400=65*144+40

i.e dividing 9400 by 65 gives a remainder 40

so , 40 should be subtracted from 9400 to get divisible by 65

(a)

8) 2505 / 0.5 = 5010 then 25.05 / 0.5 = 50.10

obserb the position of decimal

(b)

9) 1/5 and 2/5 => 200/1000 & 400/1000

so, 262/1000, 275/1000 lie betn 1/5 & 2/5

(a)

10) 2 log10 5 + log10 4 = log10(5^2*4)=log10(100)=2

(a)

11) (a-x) will decrease linearly as x increases for a greater than 1.

(b)

12) n(S)=6^2

E=getting sum 5= (1, 4), (2, 3), (3, 2), (4, 1) => n(E)=4

p=n(E)/n(S)= 4/6^2 = 1/9

(c)

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