Tuesday, August 18, 2015

AMCAT Quantitative Ability Previous Papers-11

101)Deepak sells 50 shirts at the cost price of 60 shirts.His gain percent is:
a.0.15      b.0.1        c.0.25      d.0.2
sol:    Let cost of each shirt is 100
60*100=50*x  ==>    x=120(new cost)
20%  is the profit. i.e.,    20/100 = 0.2

102)The LCM of 26 * 32 * 5 * 7, 23 * 35 * 7 and 2 * 34 * 5 is:
a.26  * 35                           b.26 * 35 * 5            c.26 * 35 * 7             d. 26 * 35 * 5 * 7
Sol:    26*35*5*7                  
Hint: Product of all primes with highest powers.

103)Find the greatest number that divides 125,218,280 and 342 so as to leave the same remainder in each case.
a.37         b.35         c.33         d.31
Sol:  Trail method.
                                (Or)
218-125=93,                           280-218=62,
280-125=155,                         324-218=124,
342-125=217,                         342-125=217
H.C.F of  93,155,217,62,124,217 is 31

104)The sum of squares of 3 numbers is 170, while the sum of their products taken two at a time is 157.What is the sum of the numbers?   a.20     b.22    c.24    d.28
            Sol:  a2+b2+c2=170,                ab+bc+ca=157
                                (a+b+c)2=a2+b2+c2+2(ab+bc+ca)
                                                 =170+2(157)
                                                 =484
                                     (a+b+c)=22

105)Eight teams are playing in a cricket match.If a team loses,it is out of the tournament.How many games are needed to determine the winner?
a.7     b.6              c.8           d.9
                Sol:   7 games are needed.
                1 1           1 1           1 1           1 1           ---    4 games
                    1            1              1              1            ---    2 games
                          1                              1                    ---    1 game
                                           1                                Total =7 games

106)What will be the value of x in the expression[ 722-282 = 50x]?
a.44         b.46         c.86         d.88
Sol: 722-282=50x     ==>     (72-28)(72+28)=50x   ==>     44*100=50x    ==>     x=88

107)There are 3 main steps of completion of a project-Development,Review and Roll out.After development, there are 4 people who can independently work and lead the process to the process to the next step i.e. Review.Further ahead,there are 5 people who can work independently and lead to the next step i.e.Roll-out.In how many ways can a project manager complete the project?
a.20         b.9           c.15         d.25         e.18
Sol:       4c1*5c1=4*5=  20                     (Combinations)

108)Find a number that can replace y in the expression (x4)0= x2/3 * xy
a. -2/3     b. 2/3      c. 1          d. 0          e.-4
Sol:   (x4)0=x2/3 *x     ==>        x0=x(2/3)+y        ==>          0=(2/3)+y      ==>     y=-2/3 

109)A group of 4 students is to be chosen from 3 boys and 5 girls.Find the probability that the group contains exactly 3 girls.
a.3/7       b.4/7       c.5/7        d.6/7
 Sol:     (5C3*3C1)/8C4    ==>  3/7

110.A cistern can be filled by two pipes A and B in 10 and 15 hours respectively and is then emptied by a tap in 8 hours.If all the taps are opened,the cistern will be fill in:
a. 21 hours              b. 22 hours              c.23 hours               d.24 hours               e.None of the above
Sol:          Time takes to fill the tank, if all pipes are opened = (1/10 )+(1/15) -(1/8)
                                                                                                =(5/120)
                                                                                                =1/24 i.e., 24 hrs to fill the tank    

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