Official Quant thread for CAT 2013

MBA CAT 2024
9881
@IIM-A2013 said:
A shopkeeper makes a profit of Q% by selling an object for rs24.Had c.p and s.p be interchanged it would have led to a loss of 62.5Q%.With the latter c.p what should be the new s.p to make a profit of Q%?a.34.4 b. 32.5 c.25.6 d.38.4please tell the approach to solve?
62.5* [24 - C]/C = [24 - C]/24
Thus, C = Rs. 15

For a Profit of 9/25, he should sell it at Rs. 32.5 [Option B]
9882
Find all prime p for which (p^2 - 1)! is divisible by p^6 but not by p^7.
9883
@Estallar12 said:
62.5* [24 - C]/C = [24 - C]/24Thus, C = Rs. 15For a Profit of 9/25, he should sell it at Rs. 32.5 [Option B]
in book it is 38.4
9884
@chillfactor said:
Find all prime p for which (p^2 - 1)! is divisible by p^6 but not by p^7.
7?

(p^2 - 1)! has p-1 multiples of p.
So if p = 7
(7^2 - 1)! will be divisible by 7^6 but not by 7^7
9885
@IIM-A2013

Given, SP of the given article=24, Profit=Q %

Thus, CP=24/(1 + Q/100)

Now, New CP=24, New SP=24/(1 + Q/100), Here, the person suffers a loss of 62.5Q%..

Thus, 625/1000*Q/100= 1 - 100/(100 +Q)..(i)

At Q=60, eqn(i) is satisfied..Thus, Q=60%..

Thus, New SP=1.6*24= 38.4..
9886
@chillfactor said:
Find all prime p for which (p^2 - 1)! is divisible by p^6 but not by p^7.

Only 7?

regards
scrabbler
9887
@chillfactor said:
Find all prime p for which (p^2 - 1)! is divisible by p^6 but not by p^7.
7
9888
@IIM-A2013 said:
A shopkeeper makes a profit of Q% by selling an object for rs24.Had c.p and s.p be interchanged it would have led to a loss of 62.5Q%.With the latter c.p what should be the new s.p to make a profit of Q%?a.34.4 b. 32.5 c.25.6 d.38.4please tell the approach to solve?
b 32.5
9889
@IIM-A2013 said:
in book it is 38.4
@Estallar12 said:
62.5* [24 - C]/C = [24 - C]/24Thus, C = Rs. 15For a Profit of 9/25, he should sell it at Rs. 32.5 [Option B]
I committed a mistake there. Infact, Blunder. :embarrassed:

Here, Q = 0.6 and so for Profit = 60 percent, SP = 1.6*24 = 38.4 Rs.
9890
@IIM-A2013 said:
A shopkeeper makes a profit of Q% by selling an object for rs24.Had c.p and s.p be interchanged it would have led to a loss of 62.5Q%.With the latter c.p what should be the new s.p to make a profit of Q%?a.34.4 b. 32.5 c.25.6 d.38.4please tell the approach to solve?

If original profit is x%, then on interchanging, the loss is 100x/(100+x) %. So in this case since original profit was Q%, loss should be 100Q/(100+Q)% but this is told to be 62.5% of Q = 5Q/8.

So 100Q/(100+Q) = 5Q/8 => 800 = 500 + 5Q => Q = 60.

So if CP is 24, SP should be 24 (1 + 0.6) = 38.4.

regards
scrabbler
9891
@scrabbler thanks 😃 but can u exaplain the solution given in the time material...

95x+77y=2724

rem2724/77 = 29 ("rem" means remainder of)

therefore rem18x/77=29 => 18x=77x1 + 29 (in "x1" 1 is the subscript)

therefore rem5x1/18=7 => 5x1=18x2 + 7

therefore rem3x2/5=3 =>3x2=5x3 + 3

therefore 2x3/3=0 =>x3=3x4

x4=0 => x3=0 => x2=1 => x1=5

=> x=(77(5) + 29)/18 =23 and y=7.

although this is very big process compared to urs which is really short and easy to grasp,but the above mentioned approach has been mentioned at many places in time material. But i am not getting it.
9892
@nole said:
@scrabbler thanks but can u exaplain the solution given in the time material...95x+77y=2724rem2724/77 = 29 ("rem" means remainder of)therefore rem18x/77=29 => 18x=77x1 + 29 (in "x1" 1 is the subscript)therefore rem5x1/18=7 => 5x1=18x2 + 7therefore rem3x2/5=3 =>3x2=5x3 + 3therefore 2x3/3=0 =>x3=3x4x4=0 => x3=0 => x2=1 => x1=5=> x=(77(5) + 29)/18 =23 and y=7.although this is very big process compared to urs which is really short and easy to grasp,but the above mentioned approach has been mentioned at many places in time material. But i am not getting it.

I'm afraid I can't, because I have no patience to apply such a long method in most cases....

I think someone above explained it (a page or two back). I didn't read it in detail, then or now, but I assume it uses the basic ideas of remainders and modulo techniques. But frankly I don't think I would want to do that much effort in the exam - the writing part alone would take over a minute and a half...and then first step mein dividing 2724 by 77....srsly, bro? Not happening.

Would rather come up with some simpler approach, like the one I gave. Or maybe if total 30 is not known, something like:

95x+77y=2724
95(x+y) = 2724 + 18y. So for LHS, which is even, to be divisible by 95 i.e. by 5 it has to end in 0. So 18y must end in 6. Then trial and error a bit, y = 2, 7, 12, 17.... answer aa jayega.

Basically in about 70-80% of such problems, there would be some simplification possible if you are really comfortable with how numbers behave and are not tied down to a formulaic approach.

(If I can't see a quicker method, would rather leave the question and move on - in the current scenario there are guaranteed to be plenty of solvable questions; why get stuck on this? Speed is my forte, accuracy goes for a toss now and then. But then even 100%ilers don't necessarily get all the questions (or even attempt all the questions) so...of course, those are my personal views, others may disagree 😃 )

regards
scrabbler
9893

one camera buy= > 3 rolls free

6 rolls buy=> 1 rolls free

6x3=18rolls buy=3 rolls free

>18Rolls buy=one camera buy

Answer=18

9894
one merchant correctly calculates his profit percentage on the cost price ;another wrongly calculates it on the selling price. find the diffrence in the actual profit if both claim to make30% profit and their revennue is Rs. 3900.
9895
@gkkshetija said:
one merchant correctly calculates his profit percentage on the cost price ;another wrongly calculates it on the selling price. find the diffrence in the actual profit if both claim to make30% profit and their revennue is Rs. 3900.
270?
9896
@gkkshetija : is it 270 ?? rs
9897
@IIM-A2013 said:
A shopkeeper makes a profit of Q% by selling an object for rs24.Had c.p and s.p be interchanged it would have led to a loss of 62.5Q%.With the latter c.p what should be the new s.p to make a profit of Q%?a.34.4 b. 32.5 c.25.6 d.38.4please tell the approach to solve?


(24-x)/C = q/100
(x-24)/24 = (-62.5q)/100


9898
@IIM-A2013 said:
A shopkeeper makes a profit of Q% by selling an object for rs24.Had c.p and s.p be interchanged it would have led to a loss of 62.5Q%.With the latter c.p what should be the new s.p to make a profit of Q%?a.34.4 b. 32.5 c.25.6 d.38.4please tell the approach to solve?
let cp = x

24-x/x=Q/100
24-x/24=62.5Q/100

solve for x
x=15
24-15/15*100=60%
Q=60%
therefore
for cp=24
sp-24/24=60%
sp=38.4??
9899
@gkkshetija said:
one merchant correctly calculates his profit percentage on the cost price ;another wrongly calculates it on the selling price. find the diffrence in the actual profit if both claim to make30% profit and their revennue is Rs. 3900.
270??

3900-x/x=30/100
x=3000
3900-3000=900

3900-y/3900=30/100
y=2730
3900-2730=1170

diff=1170-900=270


9900

In a nut-bolt factory 180 workers are working for 6 hours a day. Out of 180 there are some men, some women and rest are boys. All of them can produce either nut or bolt or either of them. A man can produce 60 nuts and 80 bolts in an hour. A woman can produce 30 nuts and 60 bolts per hour. A man is thrice as efficient as a boy and 1.5 time as efficient as a woman. Given all men and women and boys produce equal number of articles per hour (either nut or bolt)


1) Working 6 hours a day, how many nuts can they produce with 52500 bolts a day?
Answer: 50850

2) In how many hours can 15 men and 12 women and 8 boys produce 12000 nuts and 8200 bolts

Answer 5

3) If the efficiency of each boy is doubled what is the increase in production per hour

Answer 33.33%

4) If the manager of the factory wanted equal number of men, women and boys in his factory but the efficiency of a man, woman and boy remain constant, then the change in porduction is

Answer: Increase by 8.33%