Monday, August 17, 2015

AMCAT Quantitative Ability Previous Papers-7

61. 4.28 and -3.28 are two numbers on a real number line. If 1 is added to the numbers, then which of the following is true?
A. Distance between the two new numbers is 2 more than distance between 4.28 and -3.28
B. Distance between the two new numbers is 2 less than distance between 4.28 and -3.28
C. Distance between the two new numbers is 2 equal distance between 4.28 and -3.28
D. None of these

62. When a local train travels at a speed of 60 kmph. It reaches the destination on time .  when the same train travels at speed of 50kmph. It reaches its destination15 minutes late. What is the length of journey?
A. 75km   B.50km    C. 60km   D.85km

Solution:

distance is constant.
so let time taken be t when it travels with 60kmph
let time be t' when it travels with 50kmph
d=s*t
therfore
s*t=s'*t'
60*t=50*(t+15/60)(in hrs)
on solving
t=5/4 hrs
d=60*5/4
75km

63. In a shooting competition, the probability of hitting the target by P is 3/5. By Q is 1/3 and by R is 2/5. If all they fire independently at the same target calculate the probability that only one of them will hit the target.
A. 25/75           B. 32/75               C. 39/75                  D. 43/75

Solution:

ans .32/75.
P(p)=3/5 P(p')=2/5 same way for rest and by using formula
P(p)*P(q')*P(r')+P(p')*P(q)*P(r')+P(p')*P(q')*P(r)

64. For what value of M is the number 7M42876M divisible by 11?
A. 0    B. 8    C.4     D. 9

Solution:
Here an easy way to test for divisibility by 11. Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.
So, for instance, 2728 has alternating sum of digits 2-7+2-8 = -11. Since -11 is divisible by 11, so is 2728.
Similarly, for 31415, the alternating sum of digits is 3-1+4-1+5 = 10. This is not divisible by 11, so neither is 31415.

Coming to the given question,
7-M+4-2+8-7+6-M
16-2M
so if M=8 then 16-16=0 so total number is divisible by 11.

65. A group of women can finish a piece of work in 50 days. In how many days will one-third the number of women be able to finish two-third of the work?
A.        150 days       B.        75 days        C.        50 days         D.        100 days

Solution:

x women takes 50 days to complete a piece of work.
1/3 x women takes 150 days to complete a piece of work.
1/3 x women takes 100 days to complete 2/3 rd work.

66. What is the value of log512 8?
A.        3          B.        1/3                 C.        -3        D.        -1/3

Solution:
log512 8
= log512 (512)1/3
=1/3

67.      If log10 3 = 0.477, then the value of log10 9 is:
A.        1          B.        0.477             C.        0.954             D.        0.523
Solution:
log10 9= 2 log 10 3 = 2 * 0.477 = 0.954

68.      When the price of a pair of shoes is decreased by 10%, the number of pairs sold increased by 20%. What is the net effect on scales?
A.        8% decrease                        B.10% decrease      C.10% increase       D.        8% increase
ans: let cp be 100, when price decreased by 10% then sp=90. Now sales increased by 20%, ie, 90+20%of90=108.
so cp=100, sp=108, gain=8, gain%=gain*100/cp=8%increase

69.      Replace the symbols * and # in 9586*4# so that it is divisible by both 8 and 5.
A.        0,0      B.        1,0      C.        0,5      D.        1,5
Solution:
Rule for Divisible by 5 : number should end with either 0 or 5
Rule for divisible by 8: Last 3 digits should be divisible by 8
Solve from options: If option (A) is correct then number becomes 9586040
It is divisible with both 5 and 8 so Option(A) is correct.

70.      If a coin with both heads is tossed, then the probability of obtaining a tail is:
A.        0          B.        ½         C.        1/3     D.        1

Solution: If a coin contains both heads then no way we get tail so probablity is 0.

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