AMCAT Quantitative Ability Previous Papers-9

81.      For irrigational purposes, a farmer uses a tank of water. He uses a pipe during night to fill the tank, so that he could use the tank of water in the morning to irrigate his farm. The pipe fills the tank in 3 hours but on the particular day,because of a leak in the tank, the pipe takes 4.5 hours to fill it. In how many hours can the tank be completely emptied by the leak alone? 

A.        6          B.        9          C.        1.5      D.        Data insufficient

Solution:  pipe one hour capacity is 1/3 
1/3 + x = 2/9
x=9 
Answer is 9 hours.

82.      The printed price on a book is RS. 400, a bookseller offers a 10% discount on it. If he still earns a profit of 12%, then the cost price of  the book is:
A.        RS. 280                      B.        RS. 352          C.        RS.360           D.        RS.300

S.P= 360 Rs.
If Profit = 12% then 1.12*C.P = S.P
1.12*C.P = 360
C.P= 321.43 Rs.
And If Profit=12 Rs. then C.P= 348 RS.
As there is ambiguity in question.

83.      If r = at² and s = 2at, then the relation among s, r and a is:
A.        s² = 4ar          B.        s = ar              C.        s² = ar                        D.        None of the above
Solution:
r=at2
s=2at
therefore t=s/2a
r=as^2/4a^2
s^2=4ar

84. Amit bought 10 cycles for Rs1750 each. He sold four cycles for Rs8400, three for 1900 each. At what price he should sell remaining cycles so as to earn an average profit of Rs320 per cycle?
1900       2000       1800       2050       2200
Solution: 10 cycles cost price + 10 cycles profit = 10 cycles selling price
10(1750) + 10 (320) = 8400 + 3(1900) + 3 (x)
solve above equation then x = 2200

85. Out of 26, 13, and 34, which two numbers are co-primes?
26 and 14             13 and 34             26 and 34             None of the pairs are co primes
Ans:  Two numbers are said to be co-prime when their GCD is 1.
GCD( 26,13) = 13
GCD ( 26,34) = 2
GCD (13, 34) = 1
SO answer is 13 and 34.

86. A man earns 24,000 per month. He spends one-third of his income on personal expenditure. Half of the remaining income is invested in a scheme for 15% interest per annum. After investing half of the remaining income is invested in a scheme which gives 10% income per annum. The remaining lies in a bank where it earns an interest of 4% per annum. The effective rate of interest earned by the man on his investments by the end of the year is?
19%                        10%                        11%                        29%                        12.33%

Solution:

amount remaining= 24000-24000/3=16000

1. 16000/2=8000 SI=PRT/100=8000*15*1/100=1200

2. 8000/2=4000 SI=4000*10*1/100=400

3. 4000 SI=4000*4*1/100=160

adding total interest=1200+400+160=1760

SI=PRT/100 1760=16000*R*1/100

Solving this R=11% Ans......

87)A person forgets the last two digits of user ID for a website. He remember that both digits are odd. what is the probability of him typing the correct last digits by randomly typing 2 odd digits?

A)1/25                  B)1/5     C)1/2                     D)2/5

Ans: guessing one odd digit is 1/5
guessing  two odd digits is (1/5) * (1/5) = 1/25

88)Every number of housing socity contributed as much as there are numbers f members in the socity. The president added Rs.150 extra from to take the total of Rs. 2,650. How many members are there in the housing society?

A)25                       B)50       c)60        d)35

Ans: 2650 - 150 = 2500
50*50 = 2500
ans is 50.

89)Given that the interest is only earned on principal, if an investment of Rs 1000.00 amounts to Rs 1440.00 in two years, then what is the rate of interest earned?

A)20%   B)22%   c)21%    D)11%   e)44%

Solution: Interest for two years is 440
Interest for one year is 220
Apply Simple interest formula. (1000 * 1 * r )/ 100 = 220
r =22%

90)Gitu and Rashmi were playing ludo. Game starts when one gets 6 in two consecutive throws of dice. What is the probability that gitu can start the game in first chance?

A)1/6     B)1/36                   C)5/36   D)5/6

Solution: Getting 6 is 1/6
getting two 6's is (1/6) * (1/6) = 1/36

AMCAT Quantitative Ability Previous Papers-12

111)Evaluate:log(a²bc³)⁵

a. 32log a + 5log b + 243log c                        b. (10log a + 5log b + 15log c)                       c. 15(log a + log b + log c)              d. 5log (a²bc³)

Ans: (B)

112) if p varies directly as the square of q and inversely as the square root of r,which of the following would be true if k represents constant of variation?

a.p(q)² = √k        b.k= r²* p *q^-2     c.p/k(q)² =√r      d. √p =1/k(q)²

113) what is the loss percentage incurred by a company when it buys an asset for Rs 1,50,000 and sells it for Rs 75,500?

a.49.67%                              b.49.34%                              c.98.68%                              d.98.34%

A) c.p = 1,50,000rs

      s.p= 75,500

   loss = c.p – s.p

           = 1,50,000 – 75,500

           = 74,500

Loss% = (loss/c.p)*100

             = (74,500/1,50,000)*100

             = 49.67%

114)If a positive integer n is divided by 5 then the remainder is 3. Which of the following numbers gives remainder 0,when it is divided by 5?                              a.  n + 3                 b.  n – 2                                c.  n + 2                 d. n + 1

Ans: n+2;

115) Find the greatest 5 digit number that is exactly divisible by 3, 4, 5 and 7?

a.99940                 b.99960                                c.99970                 d.99990

Ans: 99999 / LCM(3,4,5,7)  = 99999 / 420 = 238 ( quotient)

238 * 420 = 99960

116)Probability of one of the power plants over heating is 0.15 per day and the probability of failure of the backup cooling system is 0.11 .If these events are independent.What is the probability of ‘big trouble’(i.e . both events taking place)?                  a.0.35                    b.0.0185                               c. 0.0165                               d.0.26

Ans:  big trouble occur when overheating and failure of cooling system happens at the same time.

0.15 * 0.11 = 0.0165

117)If the selling price of a watch is halved,the profit becomes quartered.Find the profit percentage of the watch?

a.50%                    b.66.67%                              c.100%                  d.200%

let c.p=x

        s.p=y

        ((y/2)-x)/x=((y-x)/x)*(1/4)

        y=3x

profit%=((3x-x)/x)*100

       =200%

118)Simplify the expression 7log₅ p + √3 /2 log₅ q – ½ log₅ 2r

a.log₅ p⁷ + q⁽√3^)/2 – (√2)( √r)                        b.log₅(p⁷ + q⁽√3^)/2)/r        c.log  p⁷ .q⁽√3/2⁾/(( √2)( √r))         d. log5 p⁷ . q^{(√3/2 )}– ((√2)( √r))

7logp+((3)^(1/2))/2logq-(1/2)log2r

    =logp^(7)+logq^((3^(1/2))/2)-log2r^(1/2)

    =log((p^(7)*q^((3^(1/2))/2))/(2r^(1/2))

119)There are 5 clients and 5 consultants in a round table meeting.In how many ways can the clients be seated such that no consultant is next to the other consultant?         

a. 5! 6!                  b.4! 4!                   c.4! 5!                    d.9!                        e.c5 5! 4!

Ans:  5 clients can be arranged in 4! Ways as it is a circular arrangement.

Now 5 places left in between 5 clients. So 5 consultants can be arranged in 5! Ways.

Total: 4! * 5!

120)A company decides to reorganise its financial transaction files and put all such files into various drawers. In how many ways can 7 files be put into 3 drawers ,if any number of files can be put in each drawer?

a.7³                                     b.⁷p3                     c.7!/4!                   d.3⁷                                    e.⁷c3