Problem Solving

tohellandback wrote:
A) agreed as you said

B) take the example x=21,y=14
35x=5*7*3*7
20y=4*5*2*7
GCF is 5*7 (7 is 21-14, thats what I meant when i said "depends upon the values of x and y")
C) Hold on I will give you a "big explanation"

D) possible because it is possible that between two numbers one of them can be the GCF.
I will give you an example, you figure out the rest.
y=3
=12
well, let me explain
since 20y contains 2^2, 5 and y. it can be the GCF if 35x contains all of these. now 35x already has 5 so, any value of x that contains 2^2 and as factors will make it possible

E) same explanation as above
20y already contains 5. so any value of y that has x and 7 as factors will make it possible
ex: x=3
y=21

by now I think you have understood why C is right, but still
35x=5*7*x
20x would have been possible only if there was a 2^2 in the factorization.
now you can argue that what if x has that 2^2 so precious to me
let x=4
now 20x is 2^2*5*2^2
but you original number 35x doesn't have two (2^2)s. It has only one 2^2 and that is from x. so 20x cannot divide it. Now you see why i mentioned there should be the prime numbers in the factorization.

Hope I am clear. Thanks

axat wrote:If 6xy = x2y + 9y, what is the value of xy?

(1) x = –2

(2) x < 0



Source : MGMAT

OA will follow. I know this is a DS question posted in the PS section, but I don't want start a different thread for the DS questions.

In this question, I'll appreciate it if you guys could tell me what is it that went through your minds as you solved this question.

My instinct was to solve the equation by eliminating y, which is what I did, but that gave me a value for x and left me stranded.

axat wrote:If 6xy = (x)square(y) + 9y, what is the value of xy?

(1) x = –2

(2) x < 0



Source : MGMAT

OA will follow. I know this is a DS question posted in the PS section, but I don't want start a different thread for the DS questions.

In this question, I'll appreciate it if you guys could tell me what is it that went through your minds as you solved this question.

My instinct was to solve the equation by eliminating y, which is what I did, but that gave me a value for x and left me stranded.

axat wrote:If 6xy = (x)square(y) + 9y, what is the value of xy?
(1) x = –2

(2) x < 0

tohellandback wrote:IMO C, and well i did it in <40 secs:)
so 1C+8X=257
1C+8Y=185
subtract 2 drom 1

8x-8y=72
8*1.8*y-8y=72
6.4y=72
y=72/6.4
we need to find 8y
so 8y=(72*8)/6.4==90

axat wrote:

tohellandback wrote:IMO C, and well i did it in <40 secs:)
so 1C+8X=257
1C+8Y=185
subtract 2 drom 1

8x-8y=72
8*1.8*y-8y=72
6.4y=72
y=72/6.4
we need to find 8y
so 8y=(72*8)/6.4==90

I am too embarrassed to even SHARE the stupid mistake I made. My approach was exactly the same as yours but I made an error that is reserved for those who are exclusively thick in the head.

axat wrote:Source MGMAT

Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?


A 22(2/9)%
B 16(2/3)%
C 11(1/9)%
D 10%
E 5%