either "2" or "24"

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

either "2" or "24"

by sanju09 » Tue Mar 17, 2009 3:03 am

If the terms of a series are either "2" or "24" and the sum of all the terms of the series is 124, then which of the following could be the number of "2s" in the series?

A. 48

B. 35

C. 32

D. 28

E. 26

OA E

Last edited by sanju09 on Tue Mar 17, 2009 3:24 am, edited 1 time in total.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Tue Mar 17, 2009 3:03 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Tue Mar 17, 2009 3:16 am

The key here is with 24.
Notice that:
1*24 = 24 - 100 is left for 2's, giving us 50 2's

2*24 = 48 - 76 is left for 2's, giving us 38 2's

3*24 = 72 - 52 is left for 2's, giving us 26 2's

4*24 = 96 - 28 is left for 2's, giving us 14 2's

OR you could have all 2's, with 124 = 62*2.

I'm getting two answers.... I may have done some inccorect calculations...

Quote

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

by sanju09 » Tue Mar 17, 2009 3:28 am

DanaJ wrote:The key here is with 24.
Notice that:
1*24 = 24 - 100 is left for 2's, giving us 50 2's

2*24 = 48 - 76 is left for 2's, giving us 38 2's

3*24 = 72 - 52 is left for 2's, giving us 26 2's

4*24 = 96 - 28 is left for 2's, giving us 14 2's

OR you could have all 2's, with 124 = 62*2.

I'm getting two answers.... I may have done some inccorect calculations...

Oh no DanaJ! You are absolutely correct on both your approach and calculations; necessary editing has been now made to the question. Thanks

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Quote

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pm; Thanked: 104 times; Followed by:1 members

by scoobydooby » Tue Mar 17, 2009 3:47 am

2x+24y=124
=>x+12y=62, x and y must be integers
x values given we need to find if for the given values y is an integer

y=62-x/12

A. x=48, y=14/12 not an integer

B. x=35, y=odd/12 not an integer, (even-odd=odd)

C. x=32, y=30/12 not an integer

D. x=28, y=34/12 not an integer

E. x=26, y=36/12 integer and hence E