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DS:algebra

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Source: — Data Sufficiency |
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by ajith » Thu Feb 04, 2010 6:38 am
harsh.champ wrote:Given that 'a' and 'b' are integers and
-2<(a-6)<(b-11)and
(b^2) > 9 . Find the value of 'b'.

A. b > 9
B. b < 11
1. Insufficient
2. Insufficient

only value possible is b=10 in which case a-6 will be either -2 or b-11 so not possible
Value of b cannot be found

1&2 combined also insufficient

E for me
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by Ian Stewart » Thu Feb 04, 2010 10:40 am
harsh.champ wrote:Given that 'a' and 'b' are integers and
-2<(a-6)<(b-11)and
(b^2) > 9 . Find the value of 'b'.

A. b > 9
B. b < 11
Where are these questions from? This is, as ajith points out above, mathematically impossible; it's the second of your questions I've replied to today which has no legitimate solution, and I'm curious to know their source so I can tell my students not to use it. From the stem, we know that

-2 < b - 11
9 < b

So Statement 1 tells us nothing we don't already know; it is useless, and the answer must therefore be B or E. Now, since b is an integer greater than 9, with Statement 2 we can be certain that b=10. But there's a problem; now no value of a is possible. We know that -2 < a - 6, so a > 4. But if b = 10, we also have that a-6 < 10-11, so a-6 < -1, and a < 5. That is, we must have that 4 < a < 5. That's not possible if a is an integer. There's no mathematically correct answer to this question.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by harsh.champ » Thu Feb 04, 2010 3:47 pm
Ian Stewart wrote:
harsh.champ wrote:Given that 'a' and 'b' are integers and
-2<(a-6)<(b-11)and
(b^2) > 9 . Find the value of 'b'.

A. b > 9
B. b < 11
Where are these questions from? This is, as ajith points out above, mathematically impossible; it's the second of your questions I've replied to today which has no legitimate solution, and I'm curious to know their source so I can tell my students not to use it. From the stem, we know that

-2 < b - 11
9 < b

So Statement 1 tells us nothing we don't already know; it is useless, and the answer must therefore be B or E. Now, since b is an integer greater than 9, with Statement 2 we can be certain that b=10. But there's a problem; now no value of a is possible. We know that -2 < a - 6, so a > 4. But if b = 10, we also have that a-6 < 10-11, so a-6 < -1, and a < 5. That is, we must have that 4 < a < 5. That's not possible if a is an integer. There's no mathematically correct answer to this question.
_____________________
This question was also part of my test taken by the tutor at the native place.
After reading your comments,I am really torn between what to do and what not to??
We were not provided the methods of solving the questions so i posted it on the forum to gain the insights of GMAT tutors like you .As you are suggesting that such questions are not part of the GMAT,I am doubting if I am studying under the wrong person.In the test,a lot of difficult questions surfaced up which I also thought would not be worthwhile spending time upon.
Seeking urgent help!!
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by sanju09 » Sat Feb 06, 2010 3:54 am
harsh.champ wrote:Given that 'a' and 'b' are integers and
-2<(a-6)<(b-11)and
(b^2) > 9 . Find the value of 'b'.

A. b > 9
B. b < 11
If a and b are integers and -2 < (a - 6) < (b - 11), then a > 4 and b > 9, just no need of the info that b^2 > 9.

(1) b > 9, we already know. Insufficient

(2) b < 11, with b an integer greater than 9 only tells, b = 10. Sufficient

[spoiler]B[/spoiler]

[spoiler]But, a won't exist. Can we imagine that on GMAT?[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by ajith » Sat Feb 06, 2010 4:02 am
sanju09 wrote: (2) b < 11, with b an integer greater than 9 only tells, b = 10. Sufficient
-2<(a-6)<(b-11)

If b=10; -2<(an integer)<-1; there exists no such integer! Isn't that a problem?
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by sanju09 » Sat Feb 06, 2010 4:14 am
ajith wrote:
sanju09 wrote: (2) b < 11, with b an integer greater than 9 only tells, b = 10. Sufficient
-2<(a-6)<(b-11)

If b=10; -2<(an integer)<-1; there exists no such integer! Isn't that a problem?
It certainly is, my friend. I am in a way supporting Ian's claim by making it a possible question only if we could ignore 'a', which we can't. Whatsoever is the source, it's not a GMAT problem.
The mind is everything. What you think you become. -Lord Buddha



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