DS - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

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

Redeem

DS

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

yalanand: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Wed Feb 06, 2008 7:52 am; Thanked: 2 times; GMAT Score:620

DS

by yalanand » Fri Jan 30, 2009 1:22 pm

A math test of 100 questions is scored as follows: +1 point for every question answered correctly, 0 points for every left blank, and -1/2 point for every answered incorrectly. Harry and Sally both scored 72. Did Sally leave more questions blank than Harry?

(1) Harry answered more questions incorrectly than did Sally.
(2) If the test scoring system had been changed to -1 point for every wrong answer, then Harry would have scored lower than Sally.

Quote

Source: Beat The GMAT — Data Sufficiency | Fri Jan 30, 2009 1:22 pm

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 » Fri Jan 30, 2009 2:13 pm

I'd start by looking at the whole thing in reverse order. Say you start with 100 points. For every blank, you lose 1 point. For every incorrect answer, not only do you lose one point, but you lose another 1/2 points, since incorrect answers are penalized. For every correct answer, your score just stays the same. So you get that:
number of blanks + 3/2*number of incorrect = 100 - final score.
Say hi = number of incorrect for Harry
hb = nnumber of blanks for Harry
si = number of incorrect for Sally
sb = number of blanks for Sally.

So you have that hb + 3/2hi = sb + 3/2si = 100 - 72 = 28.

Now:

1. From hb + 3/2hi = sb + 3/2si = 100 - 72 = 28 you get that:
hi = (28 - hb)*2/3
si = (28 - sb)*2/3

Since hi > si, you get that (28 - hb)*2/3 > (28 - sb)*2/3
28 - hb > 28 - sb
- hb > - sb
hb < sb.

So yes, Sally did leave more qs blank than Harry. 1. is sufficient.

2. This changes everything, from the beginning, since, if you start with 100 points, for each blank you are penalized 1 point and for each incorrect answer you are penalized 2 points. This means that:
number of blanks + 2*number of incorrect = 100 - final score.
We keep the same notations and we get that:
100 - (hb + 2hi) < 100 - (sb + 2si)
- (hb + 2hi) < - (sb + 2si)
hb + 2hi > sb + 2si
However, since we do not have any extra info, we cannot say if Sally left more blanks than Harry.

IMO A. What is the OA?

Quote

masuarezdl: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Jan 29, 2009 9:57 am; Thanked: 1 times

by masuarezdl » Fri Jan 30, 2009 7:24 pm

DanaJ wrote:I'd start by looking at the whole thing in reverse order. Say you start with 100 points. For every blank, you lose 1 point. For every incorrect answer, not only do you lose one point, but you lose another 1/2 points, since incorrect answers are penalized. For every correct answer, your score just stays the same. So you get that:
number of blanks + 3/2*number of incorrect = 100 - final score.
Say hi = number of incorrect for Harry
hb = nnumber of blanks for Harry
si = number of incorrect for Sally
sb = number of blanks for Sally.

So you have that hb + 3/2hi = sb + 3/2si = 100 - 72 = 28.

Now:

1. From hb + 3/2hi = sb + 3/2si = 100 - 72 = 28 you get that:
hi = (28 - hb)*2/3
si = (28 - sb)*2/3

Since hi > si, you get that (28 - hb)*2/3 > (28 - sb)*2/3
28 - hb > 28 - sb
- hb > - sb
hb < sb.

So yes, Sally did leave more qs blank than Harry. 1. is sufficient.

2. This changes everything, from the beginning, since, if you start with 100 points, for each blank you are penalized 1 point and for each incorrect answer you are penalized 2 points. This means that:
number of blanks + 2*number of incorrect = 100 - final score.
We keep the same notations and we get that:
100 - (hb + 2hi) < 100 - (sb + 2si)
- (hb + 2hi) < - (sb + 2si)
hb + 2hi > sb + 2si
However, since we do not have any extra info, we cannot say if Sally left more blanks than Harry.

IMO A. What is the OA?

Dana, there is one thing I dont understand. It can be possible that say for instance:

Harry scored 72 (74 correct, 4 incorrect, 22 blanks)
Sally scored 72 (73 correct, 2 incorrect, 25 blanks)

This can also happen the other way around, so I cant see the point. Can you help me out a bit? Thanks!

Quote

krisraam: Master | Next Rank: 500 Posts; Posts: 221; Joined: Wed Jan 21, 2009 10:33 am; Thanked: 12 times; Followed by:1 members

by krisraam » Fri Jan 30, 2009 9:38 pm

IMO D

A math test of 100 questions is scored as follows: +1 point for every question answered correctly, 0 points for every left blank, and -1/2 point for every answered incorrectly. Harry and Sally both scored 72. Did Sally leave more questions blank than Harry?

(1) Harry answered more questions incorrectly than did Sally.
(2) If the test scoring system had been changed to -1 point for every wrong answer, then Harry would have scored lower than Sally.

1) says harry answered more questions incorrectly than sally. So to compensate for the wrong answers harry has to answer more correct questions than sally. For every two wrong answers more than sally harry has to answer a correct question for the score to be equal. harry attempted more incorrect questions and more correct questions than sally. So harry attempted more questions than sally. Sufficient

2) Harry will score lower when the scoring system changed to -1 from -1/2. because harry answered more incorrect questions than sally. whoever answers more incorrect questions will leave less questions blank. Sufficient

D is the answer

-raama

Quote

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 » Fri Jan 30, 2009 11:32 pm

masuarezdl: Well, in stmt 1, it is clearly stated that Harry has more incorrect answers than Sally, so your version of the results is consistent with this stmt. However, if we take it the other way, it's not consistent with this fact.

krisraam: 2) Harry will score lower when the scoring system changed to -1 from -1/2. because harry answered more incorrect questions than sally. whoever answers more incorrect questions will leave less questions blank.

Why do you assume that Harry answered more incorrect questions than Sally? That is not necessarily true.

Quote

ontopofit: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Sun Dec 21, 2008 12:00 am; Thanked: 3 times

by ontopofit » Sat Jan 31, 2009 12:54 am

Accoding to me D should be the answer.
There is no doubt that 1) satisy for this.

2) states that harry would have scored lower if incorrect answer would have cost -1 instead of -1/2.Now suppose both answered 72 correct and rest blank,then blanks are same for both.The main thing here is that if incorrect answer cost more then harry would get less mark.that means harry will be the one paying more for that.hence harry would have had more incorrect.I dont think there is a possibility that this situation can happen with harry scoring less incorrect.so statement 2) also satisfies.
hence D.
am i right?

Quote

yalanand: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Wed Feb 06, 2008 7:52 am; Thanked: 2 times; GMAT Score:620

by yalanand » Sat Jan 31, 2009 1:12 am

Statement (1) says that Harry got more questions incorrect than did Sally. If we combine that with the fact that they both received the same score, it can only mean one thing: that Harry also answered more questions correctly than did Sally. If Harry had more incorrect and more correct answers than Sally, it means that Sally left a lot more questions blank. So statement (1) is sufficient to answer the question.

Statement (2) tells us that Harry would have gotten a lower math test score than Sally had the penalty for wrong answers been greater. This tells us that he answered more questions incorrectly than did Sally. Using the analysis for statement (1), we can conclude that (2) is also sufficient to answer the question.

Since either statement by itself is sufficient, the answer is D.

Quote

masuarezdl: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Jan 29, 2009 9:57 am; Thanked: 1 times

by masuarezdl » Sat Jan 31, 2009 8:18 am

ontopofit wrote:Accoding to me D should be the answer.
There is no doubt that 1) satisy for this.

2) states that harry would have scored lower if incorrect answer would have cost -1 instead of -1/2.Now suppose both answered 72 correct and rest blank,then blanks are same for both.The main thing here is that if incorrect answer cost more then harry would get less mark.that means harry will be the one paying more for that.hence harry would have had more incorrect.I dont think there is a possibility that this situation can happen with harry scoring less incorrect.so statement 2) also satisfies.
hence D.
am i right?

Onfopofit, I think Dana is right. In the second statement, they do not specify who got more questions wrong. They just talk about the change in the scoring system.

Statement 2 is not sufficint unless you know that Harry or Sally will be affected on this change (Statement 1).

Hope it helps.

Quote

krisraam: Master | Next Rank: 500 Posts; Posts: 221; Joined: Wed Jan 21, 2009 10:33 am; Thanked: 12 times; Followed by:1 members

by krisraam » Sat Jan 31, 2009 9:20 am

DanaJ wrote:masuarezdl: Well, in stmt 1, it is clearly stated that Harry has more incorrect answers than Sally, so your version of the results is consistent with this stmt. However, if we take it the other way, it's not consistent with this fact.

krisraam: 2) Harry will score lower when the scoring system changed to -1 from -1/2. because harry answered more incorrect questions than sally. whoever answers more incorrect questions will leave less questions blank.

Why do you assume that Harry answered more incorrect questions than Sally? That is not necessarily true.

Lets assume both answered same no of correct and incorrect questions for the score to be 72.

The No. of incorrect questions is directly proportional to correct questions.
ie if no. of incorrect questions increase. no. of correct questions will also increase. If we know know who answered more no. of incorrect questions we have got our answer.

When the scoring changed from -1/2 to -1 harry lost. Had harry answered the same number of incorrect questions as sally ( he should have answered the same number of correct questions too), he will not score lower. He scored lower means he answered more incorrect questions. Harry has answered more incorrect answers than sally.

Thanks
raama

Quote

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