BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

DS: Divisibility

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 181
Joined: Fri Sep 04, 2009 12:06 pm
Thanked: 17 times
Followed by:1 members

DS: Divisibility

by ikaplan » Mon Sep 19, 2011 8:18 am
If m and n are positive integers, then is 5m+2n divisible by 3m+n?

(1) m is divisible by n
(2) m is divisible by 15 and n is divisible by 2

OA is B

Source: NOVA's GMAT DS Prep Course, p.135

The explanation in the book is very long. I tried to solve this one by testing numbers, but it took me more than 3-4 minutes. Is there any shortcut to solve this one?
"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 am
Location: India
Thanked: 310 times
Followed by:123 members
GMAT Score:750

by cans » Mon Sep 19, 2011 9:20 am
B) m=15x and n=2y
75x+4y / 45x+2y.
75x+4y = p(45x+2y)
(75-45p)x = (2p-4)y
x = (2p-4)/(75-45p) *y
m,n positive. thus (2p-4)/(75-45p) also positive.
either (2p-4)<0 &(75-45p)<0 or (2p-4)>0 & (75-45p)>0
either: p<2. but p is positive integer. thus p=1.75-45=30<0 false. thus p is not equal to 1.
or: p>2. but then (75-45p)>0 is false. Thus no solution.
Thus not divisible.
Sufficient

A) m=nx.
5x+2 / 3x+1
5x+2 = p(3x+1)
x = p-2 / 5-3p
x>0
either: p>2 and 5-3p>0 not possible.
or p<2 5-3p<0 not possible.
IMO D
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Post new topic Post Reply
• Page 1 of 1