DS OG 12 # 152

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 am; Thanked: 2 times; Followed by:1 members

DS OG 12 # 152

by HPengineer » Thu Aug 12, 2010 8:39 pm

If Carmen had 12 more tapes she would have twice as many tapes as Rafael. Does Carmen have fewer tapes then Rafael?

S1. Rafael has more then 5 tapes
S2. Carmen has fewer than 12 tapes

I got this right however i think it was by accident. Any one care to share their approach with me and so we can compare?

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 12, 2010 8:39 pm

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 » Thu Aug 12, 2010 9:04 pm

HPengineer wrote:If Carmen had 12 more tapes she would have twice as many tapes as Rafael. Does Carmen have fewer tapes then Rafael?

S1. Rafael has more then 5 tapes
S2. Carmen has fewer than 12 tapes

I got this right however i think it was by accident. Any one care to share their approach with me and so we can compare?

Take C + 12 = 2 R from stem. C will always be EVEN as C and R are whole numbers. Then try answering if C < R.

S1. If R > 5, then C + 12 is at least 12 as C and R are whole numbers. When R is 6, C is 0, making C < R as true, but when R is 12, C = R. So insufficient

S2. If C < 12, then it can at most be 10 to ensure C and R are whole numbers. When C is 10, R is 11, making C < R as true, which remains as true for all smaller possibilities for C. [spoiler]So sufficient

B[/spoiler]

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 am; Thanked: 85 times; Followed by:3 members

by clock60 » Fri Aug 13, 2010 12:15 pm

also got B
the number of tapes Carmen-c
the number of tapes Rafael-r
we are given
c+12=2r
r=c/2+6
and asked if r>c, or
(c/2+6)-c>0
c+12-2c>0
is c<12
(1) insuffiicent, here to answer definitely we need to prove that r<12, but given that r>5
(2) c<12 suffiicent

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 am; Thanked: 2 times; Followed by:1 members

by HPengineer » Sat Aug 14, 2010 3:50 am

Ok heres how i solved it... Im wondering if its dangerous to solve similar probems with out inequalities...

S1. Rafael has more then 5 tapes

C + 12 = 2R so plug 6 in for R and solve for C which = 0 so less tapes then Rafael

Now try a larger number say 20 for R and you will get C = 38 which is more tapes then Rafaeal therefore S1 is Insuff.

S2. Carmen has fewer than 12 tapes

Here i simply plugged in 11 for C and solved for R

11+12= 2R or 23/2 = R so R = 11.5 which is greater then C so statement is sufficient.

What troubled me here is that i did not get a integer for R... How can you have half a tape? Shouldnt this be a hidden constraint problem since were dealing with items?