Official Quant thread for CAT 2013

MBA CAT 2024
4901
@sujamait said:
The function f(x, y), defined on the set of ordered pairs of positive integers, satisfies the following properties.f(x, x) = xy — f(x, y) = x — f(y, x)(x + y)f(x, y) = yf(x, x + y).Find f(14, 52).OPTIONS1) 378 2) 456 3) 364 4) 728 5) None of these
none of these?

getting 2548..
4902
@sujamait said:
The average marks of section A students are 20% less than the average marks of section B students. On the other hand, the total marks of section A are 20% more than the total marks of section B. Thus, the number of students in section B is what percent of the number of students in section A?OPTIONS1) 4% 2) 150% 3) 25% 4) None of these
4) none of these

A = 0.8B
na * A = 1.2 * nb * B
na * 0.8B = 1.2 * nb * B
nb = 0.8/1.2 * na
nb = 66.67% of na
4903
@soumitrabengeri said:
If n is a natural number, then what is the sum of all the possible distinct remainders when
8^n + 7^n + 3^n + 2^n is divided by 10?

(a) 6
(b) 10
(c) 2
(d) 0

n can be 4k, 4k+1, 4k+2 or 4k+3..
when n is 4k: remainder = 4
4k+1: remainder = 0
4k+2: remainder = 6
4k+3: remainder = 0
so sum = 10
4904
@sujamait said:
The function f(x, y), defined on the set of ordered pairs of positive integers, satisfies the following properties.f(x, x) = xy — f(x, y) = x — f(y, x)(x + y)f(x, y) = yf(x, x + y).Find f(14, 52).OPTIONS1) 378 2) 456 3) 364 4) 728 5) None of these
5) None of these?

f(14,52) = f(14, 14 + 38)
= 1/38 * 38 * f(14, 14 + 38)
= 1/38 * 52 * f(14, 38)
= 1/38 * 52 * 1/24 * 24 * f(14, 14 + 24)
= 1/38 * 52 * 1/24 * 38 * f(14, 24)
= 52/24 * 1/10 * 10 * f(14, 14 + 10)
= 52/240 * 24 * f(14,10)
= 52/10 * f(14,10)
= 52/100 * 10 * f(14,10)
= 52/100 * 14 * f(10,14)
= 52/100 * 14 * 1/4 * 4 * f(10,10 + 4)
= 52/100 * 14 * 1/4 * 14 * f(10,4)
= 13 * 14 * 14 /100 * 1/4 * 10 * f(4,10)
= 13 * 7 * 7 / 10 * f(4, 4 + 6)
= 13 * 7 * 7 / 10 * 1/6 * 10 * f(4,6)
= 13 * 7 * 7 * 1/6 * f(4, 4 + 2)
= 13 * 7 * 7 * 1/6 * 1/2 * 6 * f(4,2)
= 13 * 7 * 7 * 1/2 * 2 * f(2,4)
= 13 * 7 * 7 * f(2, 2+2)
= 13 * 7 * 7 * 1/2 * 4 * f(2,2)
= 13 * 7 * 7 * 2 * 2
= 2548

PS: I'm sure there is a shorter method :P
4905
@sujamait said:
The function
f
(
x
,
y
), defined on the set of ordered pairs of positive integers, satisfies the following properties.

f
(
x
,
x
) =
x


y
—
f
(
x
,
y
) =
x
—
f
(
y
,
x
)

(
x
+
y
)
f
(
x
,
y
) =
yf
(
x
,
x
+
y
).

Find
f
(14, 52).
OPTIONS

1) 378
2) 456
3) 364
4) 728
5) None of these
Is it NOT? I'm getting 13*14^2 = 2548..
After several simplifications you'll get f(2,2).. I'm in office so can't type the whole thing!
4906
@sujamait said:
The average marks of section A students are 20% less than the average marks of section B students. On the other hand, the total marks of section A are 20% more than the total marks of section B. Thus, the number of students in section B is what percent of the number of students in section A?
OPTIONS

1) 4%
2) 150%
3) 25%
4) None of these
NOT again?
I'm getting 66.66%
4907
@sujamait said:
The average marks of section A students are 20% less than the average marks of section B students. On the other hand, the total marks of section A are 20% more than the total marks of section B. Thus, the number of students in section B is what percent of the number of students in section A?OPTIONS1) 4% 2) 150% 3) 25% 4) None of these
Avg marks of B = a
Avg marks of A = 0.8a

Total marks of B = b
Total marks of A = 1.2b

Number of students in A = 1.5 b/a
Number of students in B = b/a

% = b/a / 1.5b/a = 2/3 = 66.6%

NONE OF THESE
4908
@SarayuSheshadri sote nahi ka yaar.....good morning puys..
4909
@mailtoankit said:
@SarayuSheshadri sote nahi ka yaar.....good morning puys..
Arree noo.. I go home on weekends and come back to bangalore on Monday directly to office..
Yesterday I lost track of time and was awake till 1.. had to wake up at 3 so didn't sleep :P
4910
The climb from the foot to the top of a hill is 800 m. Amar climbs at 16 m/min and rests for 2 minutes or 20 m in 2 min and rest for 1 minute.If Amar has to reach the top in exactly 2 hours, what is the maximum number of rests that he can take?
(a) 40 (b) 41 (c) 39 (d) 38
4911
@sujamait said:
The average marks of section A students are 20% less than the average marks of section B students. On the other hand, the total marks of section A are 20% more than the total marks of section B. Thus, the number of students in section B is what percent of the number of students in section A?OPTIONS1) 4% 2) 150% 3) 25% 4) None of these
None of these... 66.67%??
4912
@19rsb said:
The climb from the foot to the top of a hill is 800 m. Amar climbs at 16 m/min and rests for 2 minutes or 20 m in 2 min and rest for 1 minute.If Amar has to reach the top in exactly 2 hours, what is the maximum number of rests that he can take?(a) 40 (b) 41 (c) 39 (d) 38
40 rests of 1 min each..
4913
@19rsb said:
The climb from the foot to the top of a hill is 800 m. Amar climbs at 16 m/min and rests for 2 minutes or 20 m in 2 min and rest for 1 minute.If Amar has to reach the top in exactly 2 hours, what is the maximum number of rests that he can take?(a) 40 (b) 41 (c) 39 (d) 38
39?
4914
@19rsb said:
The climb from the foot to the top of a hill is 800 m. Amar climbs at 16 m/min and rests for 2 minutes or 20 m in 2 min and rest for 1 minute.If Amar has to reach the top in exactly 2 hours, what is the maximum number of rests that he can take?(a) 40 (b) 41 (c) 39 (d) 38
40?
4915
@SarayuSheshadri said:
40 rests of 1 min each..
Isnt the 40th rest is when he reaches top?
4916
@adwaitjw said:
Isnt the 40th rest is when he reaches top?
ya.. I realized it now.. :P
4917
@SarayuSheshadri said:
40 rests of 1 min each..
@adwaitjw said:
39?
@ScareCrow28 said:
40?
OA 40 hai......but I'm confused between 39& 40........tell me ur approaches at least......
4918
@soumitrabengeri said:
If n is a natural number, then what is the sum of all the possible distinct remainders when8^n + 7^n + 3^n + 2^n is divided by 10?(a) 6 (b) 10(c) 2 (d) 0
i'll go for 10...
4919
@19rsb said:
OA 40 hai......but I'm confused between 39& 40........tell me ur approaches at least......
See..First we need to calculate for 16m/min speed...
time required for covering 800m = 800/16=50 min..hence rest of the time he rests..so he rests for 70/2= 35 times
If speed = 20m/2min..It takes 80min to travel 800mtrs..rest of the time i.e, 40 minutes he has to rest since total should be 120 minutes
So he rests for 40 minutes..(4o times)
4920
@19rsb said:
OA 40 hai......but I'm confused between 39& 40........tell me ur approaches at least......
Maximum number of rests he'll get if he travels at 16 m/min..
At this worst case scenario he takes 150 mins to climb..
Now for each 80m you change from 16m/min to 20m/2min he gains 3 mins..
So if he has to reach in 120 mins I need to take 10 *80m from 16m/min.. in other words he travels entire journey at 20m/2min..