Official Quant thread for CAT 2013

MBA CAT 2024
9521
@tmohan02 said:
The greatest number which will divide: 4003, 4136 and 4249:a) 43b) 41c) 45d) None of these
d) None of these?

4003 = pN
4136 = qN
4249 = rN

4136 - 4003 = (q-p)N
133 = (q-p)N

From options, N cannot be 43,41,45
9522

the ratio of jim's salary for october to his salary for november was 1.5:1.333 and the ratio of salary for november to that of december was 2:2.6666. the worker got 40 rs more for december than for october and received a bonus constituting 40% of the salary for three months. find the bonus(Assume that no of work days are same in every month)

a 368.888 rs b.152.5555 rs c.222.22 rs d. 256.6 rs
9523
@grkkrg said:
D) none?
Correct ... 😃 How did you solve this ??
9524
9525
@ron123 said:
Correct ... How did you solve this ??
Don't have a good approach.. :(
From the figure 5b > 2(a+b) .... (assuming the figure is drawn to scale)

Now from options..
take a = 2, b = 1 => 2(a+b) = 6 and 5b = 5
take a = 4, b = 1 => 2(a+b) = 10 and 5b = 5
take a = 1, b = 4 => 2(a+b) = 10 and 5b = 20
Now angle A >= 90 degrees
tan 60 = rt(3) > 1/2
So none..
9526
@IIM-A2013 said:
the ratio of jim's salary for october to his salary for november was 1.5:1.333 andthe ratio of salary for november to that of december was 2:2.6666. the worker got 40 rs more for december than for october and received a bonus constituting 40% of the salary for three months. find the bonus(Assume that no of work days are same in every month)a 368.888 rs b.152.5555 rs c.222.22 rs d. 256.6 rs

1.5:1.333---> october to november
2:2.6666--> november to dec
Combining the 2 ratio's (multiplying 1 by 3 and 2 by 2)
4.5 : 4 : 5.3332
Diff between dec and october = Rs.40
5.3332 - 4.5 = Rs.40
0.8332 = 40
1 = x

x = 40*1/0.8332
x = 48
Total salary = 48*4.5+48*4+48*5.3332 = 664
40% of 664 = bonus
bonus = 266 (approx)

Please tell me where i am going wrong
9527
@grkkrg said:
Don't have a good approach.. From the figure 5b > 2(a+b) .... (assuming the figure is drawn to scale)Now from options..take a = 2, b = 1 => 2(a+b) = 6 and 5b = 5take a = 4, b = 1 => 2(a+b) = 10 and 5b = 5take a = 1, b = 4 => 2(a+b) = 10 and 5b = 20Now angle A >= 90 degreestan 60 = rt(3) > 1/2So none..
How's angle A>=90??
9528
@soumitrabengeri said:
1.5:1.333---> october to november2:2.6666--> november to decCombining the 2 ratio's (multiplying 1 by 3 and 2 by 2)4.5 : 4 : 5.3332Diff between dec and october = Rs.405.3332 - 4.5 = Rs.400.8332 = 401 = xx = 40*1/0.8332x = 48Total salary = 48*4.5+48*4+48*5.3332 = 66440% of 664 = bonusbonus = 266 (approx)Please tell me where i am going wrong
bhai me too getting 265.6.....but in d absence of option I'm in d dubious state of mind
9529
@gnehagarg said:
Three coins are tossed. Describe
Please note:
Mutually Exclusive => No element in common.
Exhaustive => Covering all possible elements of the sample space.

@gnehagarg said:
(i) Two events which are mutually exclusive.
All three heads, all three tails
@gnehagarg said:
(ii) Three events which are mutually exclusive and exhaustive.
No head, One head, More than one head.
OR
No two consecutive tosses same, Exactly two consecutive tosses same, All three tosses same
@gnehagarg said:
(iii) Two events, which are not mutually exclusive.

At least one head, At least one tail

@gnehagarg said:
(iv) Two events which are mutually exclusive but not exhaustive.

All three heads, all three tails
@gnehagarg said:
(v) Three events which are mutually exclusive but not exhaustive.

No head, One head, Two heads

regards
scrabbler
9530
Find the greatest number, which will divide 215, 167 & 135 so as to leave the same remainder in each case.
9531
@ron123 said:
How's angle A>=90??
again from figure :P
this isn't the right approach though..
9532
@IIM-A2013 said:
In a village consisting of p persons , x% can read and write. of the males alone y%,and of the females alone z% can read and write.find the number of males in the village in terms of p,x,y and z if za.p(x-z)/(y+x-z) b.p(x-z)/(y+x-2z) c.p(y-x)/(x-z) d. p(x-z)/(y-z).tell me the approach how to solve this type of problems in exam?

Let the number of males be m, then the number of females will be p-m.
Now consider that the overall literacy x is a weighted average of y and z, so apply (for instance) alligation:

y..............z
........x
m.............(p-m)

(The dots are for formatting, please don't get confused 😃 )

So (y-x) / (x-z) = (p-m) / m.

Cross multiply and solve, you will get m = p (x-z) / (y-z)

With some comfort with weighted averages, you might be able to do it with far less calculation.

regards
scrabbler
9533
@tmohan02 said:
The greatest number which will divide: 4003, 4136 and 4249:
a) 43
b) 41
c) 45
d) None of these
D) none of these ?
9534
@tmohan02 said:
Find the greatest number, which will divide 215, 167 & 135 so as to leave the same remainder in each case.
16?
9535
Yes..... Ans:- 16.

19rsb: How did you do?.. Any method other than applying the answers.

My method:-

215 = np+x
167 = nq+x
135 = nr+x

32 = n (q+r)
48 = n (p+q)
80 = n (p+r)

So, 'n' must be 16.


Any other simply way to do this????
9536
@IIM-A2013 said:
the ratio of jim's salary for october to his salary for november was 1.5:1.333 andthe ratio of salary for november to that of december was 2:2.6666. the worker got 40 rs more for december than for october and received a bonus constituting 40% of the salary for three months. find the bonus(Assume that no of work days are same in every month)a 368.888 rs b.152.5555 rs c.222.22 rs d. 256.6 rs
option d ?

salary in Oct = 3/2 * x
salary in Nov = 4/3 * x

salary in Nov = 2y
salary in Dec = 8/3 * y


2y = 4/3 *x
8/3 * y = 16/9 * x

16x/9 - 3x/2 = 40
5x/18 = 40
x = 144

Total salary = 216 + 192 + 256 = 664
Bonus = 40% of total salary = 265.6

@soumitrabengeri I think there's a typo in the question. :)
9537
@tmohan02 said:
Find the greatest number, which will divide 215, 167 & 135 so as to leave the same remainder in each case.
215 = N*a + r ...(1)
167 = N*b + r ...(2)
135 = N*c + r ...(3)

(1) - (2) => 48 = N*(a-b)

(2) - (3) => 32 = N*(b-c)

Now, N is a factor of both 48 and 32, and since we need the highest such number -> HCF(48,32) = 16 ?
9538
@grkkrg said:
option d ?salary in Oct = 3/2 * xsalary in Nov = 4/3 * xsalary in Nov = 2ysalary in Dec = 8/3 * y2y = 4/3 *x8/3 * y = 16/9 * x16x/9 - 3x/2 = 405x/18 = 40x = 144Total salary = 216 + 192 + 256 = 664Bonus = 40% of total salary = 265.6@soumitrabengeri I think there's a typo in the question.

Yeah..even i think so..
9539

@tmohan02 said:
Yes..... Ans:- 16. 19rsb: How did you do?.. Any method other than applying the answers.
@tmohan02 said:
Find the greatest number, which will divide 215, 167 & 135 so as to leave the same remainder in each case.

See the differences 215 - 167 = 48, 167 - 135 = 32. HCF of these will give the answer (think about it and you will see why!)

regards
scrabbler
9540
@tmohan02 said:
Yes..... Ans:- 16. 19rsb: How did you do?.. Any method other than applying the answers.
16 i think

215=N*a1+k
167=N*a2+k
135=N*a3+k

N(a2-a3)=32
N(a1-a2)=48

hcf of 32 and 48 is 16