inequality

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 am; Thanked: 17 times; Followed by:1 members

inequality

by rahul.s » Sun Jan 31, 2010 2:39 am

50 = 3a + 2b

7 > |-a|

If a and b are both integers, how many possible solutions are there to the system above?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

OA: D

Last edited by rahul.s on Sun Jan 31, 2010 2:55 am, edited 1 time in total.

Quote

Source: Beat The GMAT — Problem Solving | Sun Jan 31, 2010 2:39 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Sun Jan 31, 2010 2:50 am

rahul.s wrote:50 = 3a + 2b

7 > |-a|

If a and b are both integers, how many possible solutions are there to the system above?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

OA: D

The options for a are {-6,-5,....0,.....4,5,6}

a cant be odd since if a is odd b cannot be an integer (3a+2b =50)

so a can be {-6,-4, -2,0,2,4,6}

So 7 possible solutions

Always borrow money from a pessimist, he doesn't expect to be paid back.

Quote

sars72: Master | Next Rank: 500 Posts; Posts: 241; Joined: Wed Jan 27, 2010 10:10 pm; Location: Chennai; Thanked: 23 times; Followed by:2 members; GMAT Score:690

by sars72 » Sun Jan 31, 2010 2:55 am

i assume the second statement is 7 > mod(a) where mod stands for modulus

so, we have 50 = 3a+2b and -7<a<7

-> 2b = (50-3a) -> b = (50-3a)/ 2

Since b has to be an integer, the result of (50-3a) should be even i.e. divisible by 2

So, that leaves us with the possibile values of a as -6,-4,-2,0,2,4,6

Therefore there are 7 possible values of a and thus 7 pussible values for b

So, the answer is 7