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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 3:32 am

If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

1. The largest account is $1.3 million.

2. One of the accounts is $0.7 million.

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
4. Each statement alone is sufficient to answer the question.
5. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the
statements.

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Source: Beat The GMAT — Data Sufficiency | Thu Feb 04, 2010 3:32 am

ramsharma: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sat Jan 02, 2010 9:21 am; Location: mumbai; Thanked: 3 times; GMAT Score:540

by ramsharma » Thu Feb 04, 2010 3:37 am

Statement 1: no info about other two account
Statement 2:same as one

combined 1 and 2,two accounts known,third can be taken out.(all three together is 3 million.

IMO C

RAM SHARMA

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 4:50 am

ramsharma wrote:Statement 1: no info about other two account
Statement 2:same as one

combined 1 and 2,two accounts known,third can be taken out.(all three together is 3 million.

IMO C

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

by ajith » Thu Feb 04, 2010 5:41 am

harsh.champ wrote:If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

1. The largest account is $1.3 million.

2. One of the accounts is $0.7 million.

1. Insufficient
2. Insufficient

1&2 combined (x+1.3+0.7)/3 = 1
x = 1

Sufficient

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

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ramsharma: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sat Jan 02, 2010 9:21 am; Location: mumbai; Thanked: 3 times; GMAT Score:540

by ramsharma » Thu Feb 04, 2010 6:42 am

_______________________
Statement 2:But if one of the accounts is $0.7 million,that means the sum of the rest two is $2.3 million.
Now,suppose the smallest account is $0.5 million.
That means the largest account being $1.8 million.

Hence,combining the two statements,we get the answer.
This was my way of solving it.

Is it Ok to go with the n equations,n variables rule ["two accounts known,third can be taken out"]
Yesterday,I was cautioned by a gmat tutor that it is better to spend an extra minute solving the question rather than using the above rule as in some cases it can prove wrong.

Can you just guide me over here?? {a bit confused}[/quote]

Hi Harsh.champ

It is always better to solve a question to be hundred percent sure.But sometimes it is very easy to make out that the solution exist even without actually solving the question.Somebody with math background will be able to it faster and without math background will take a little extra time.You have to be very careful while solving the simultaneous equations.
This question in fact not that type,here only a+b+c=k,where you know a,b,and k and you have find out the c. but where
ax+by=c
dx+ey=f where a,b,c,d,e,f are constant.In this case you have to be careful for solution.

RAM SHARMA

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Feb 04, 2010 10:01 am

harsh.champ wrote: Is it Ok to go with the n equations,n variables rule ["two accounts known,third can be taken out"]
Yesterday,I was cautioned by a gmat tutor that it is better to spend an extra minute solving the question rather than using the above rule as in some cases it can prove wrong.

Can you just guide me over here?? {a bit confused}

That was me, I think. I can modify the question in the original post to illustrate why it can be dangerous to simply count equations and unknowns; the example below is quite similar to many real GMAT questions I've seen:

If the average amount of money contained in three accounts is $1 million, does the smallest account contain less than $500,000?

1. The largest account contains $1.4 million.

2. The second largest account contains $1.3 million.

I imagine some test takers will look at this question rather quickly, and see that by combining the two statements that we know the amount in the smallest account -- it would be $300,000 -- and choose C. C is not, however, the correct answer. Certainly S1 is not sufficient; the other two accounts might contain $800,000 each, or one might contain $1.3m, the other $300,000. S2 is, however, sufficient. If the second largest account contains $1.3m, the largest contains at least $1.3m, so the two largest accounts contain at least $2.6m, and the smallest must contain at most $400,000, so we can answer the question with S2 alone, and the answer is B.

Most often this 'verification' step takes very little time, and you can avoid many GMAT traps by completing it.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 3:53 pm

Ian Stewart wrote:
harsh.champ wrote: Is it Ok to go with the n equations,n variables rule ["two accounts known,third can be taken out"]
Yesterday,I was cautioned by a gmat tutor that it is better to spend an extra minute solving the question rather than using the above rule as in some cases it can prove wrong.

Can you just guide me over here?? {a bit confused}
That was me, I think. I can modify the question in the original post to illustrate why it can be dangerous to simply count equations and unknowns; the example below is quite similar to many real GMAT questions I've seen:

If the average amount of money contained in three accounts is $1 million, does the smallest account contain less than $500,000?

1. The largest account contains $1.4 million.

2. The second largest account contains $1.3 million.

I imagine some test takers will look at this question rather quickly, and see that by combining the two statements that we know the amount in the smallest account -- it would be $300,000 -- and choose C. C is not, however, the correct answer. Certainly S1 is not sufficient; the other two accounts might contain $800,000 each, or one might contain $1.3m, the other $300,000. S2 is, however, sufficient. If the second largest account contains $1.3m, the largest contains at least $1.3m, so the two largest accounts contain at least $2.6m, and the smallest must contain at most $400,000, so we can answer the question with S2 alone, and the answer is B.

Most often this 'verification' step takes very little time, and you can avoid many GMAT traps by completing it.

_______
Hey Ian,
I remember it was indeed you who pointed out this trap in a Quant problem.
Rightly pointed out by you some test takers might go for the option "C".Also,I agree it is better to invest an extra minute or two and be 100%sure than to save that time and proceed further with 70-80% accuracy.

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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 » Fri Feb 05, 2010 5:49 am

If I were to quote Ian's corrected question

If the average amount of money contained in three accounts is $1 million, does the smallest account contain less than $500,000?

1. The largest account contains $1.4 million.

2. The second largest account contains $1.3 million.

then we can have, the largest, next largest, and the smallest accounts as A1, A2, and A3, respectively, such that A1 + A2 + A3 = 3000000, with the main question: Is A3 < 500000?

(1) A1 = 1400000.

or A2 + A3 = 1600000.

hence, A3 may or may not be less than 500000. Insufficient

(2) A2 = 1300000.

and A2 < A3

hence, A2 + A3 > 2600000.

or A3 < 400000. Sufficient

[spoiler]B[/spoiler]

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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