did Marta buy?

Expert replies

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Apr 08, 2009 3:58 am

Marta bought several pencils. If each pencil was either a 23-cent pencil or a 21-cent pencil, how many 23-cent pencils did Marta buy?

(1) Marta bought a total of 6 pencils.

(2) The total value of the pencils Marta bought was 130 cents.

[spoiler]OA C; IMO B[/spoiler]

Last edited by sanju09 on Wed Apr 08, 2009 11:39 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 08, 2009 3:58 am

sacx: Master | Next Rank: 500 Posts; Posts: 139; Joined: Wed Oct 22, 2008 4:36 am; Thanked: 17 times

by sacx » Wed Apr 08, 2009 7:16 am

Let a be the number of pencils costing 23 cents and b costing 21 cents

Stmt I

a +b = 6

insuff

Stmt II

23a+21b = 130

insuff

stmt I&II

solve for a and b

Suff

C

SACX

rossmj: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Feb 26, 2009 12:50 pm; Location: Chicago; Thanked: 3 times

by rossmj » Wed Apr 08, 2009 10:09 am

I get B.

23a+21b=130 where a & b must be integers >= 0 because they are pencils.

if a=o then 21b=130 so b does not = an integer
if a=1 then 21b=107 so b does not = an integer
if a=2 then 21b=84 so b=4
if a=3 then 21b=61 so b does not = an integer
if a=4 then 21b=38 so b does not = an integer
if a=5 then 21b=15 so b does not = an integer

gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Wed Apr 08, 2009 10:44 am

if a=o then 21b=130 so b does not = an integer
if a=1 then 21b=107 so b does not = an integer
if a=2 then 21b=84 so b=4
if a=3 then 21b=61 so b does not = an integer
if a=4 then 21b=38 so b does not = an integer
if a=5 then 21b=15 so b does not = an integer

There is a flaw in your reasoning

As you said you are getting B as answer
This means (2) is suff for you

but as you have solved,you have used some value of a to get a value of b,am I right??

this means you need to have some value of a to solve this equation and you cannot solve solely on the equation given by statement (2)

Hope this helps

karan

Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Wed Apr 08, 2009 10:47 am

Iam getting B as well , and for the same reasons as Ross showed in the previous posts.

For love, not money.

Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Wed Apr 08, 2009 10:50 am

gmat740 wrote:
if a=o then 21b=130 so b does not = an integer
if a=1 then 21b=107 so b does not = an integer
if a=2 then 21b=84 so b=4
if a=3 then 21b=61 so b does not = an integer
if a=4 then 21b=38 so b does not = an integer
if a=5 then 21b=15 so b does not = an integer

There is a flaw in your reasoning

As you said you are getting B as answer
This means (2) is suff for you

but as you have solved,you have used some value of a to get a value of b,am I right??

this means you need to have some value of a to solve this equation and you cannot solve solely on the equation given by statement (2)

Hope this helps

karan

This is not necessarily true Karan,

We know that "a" and "b" are VARAIBLES......except they are both INTEGERS as well (cannot have fractional pencils...a favorite GMAT trick on 600 + questions).

The only way to get 130 from a combination of 23 cents and 21 cents is to have 2 , 23 cent pencils and 4, 21 cent pencils.

Unique answer implies sufficiency.

For love, not money.

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