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# Is 0< a/b < 1?

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Intern
Joined: 13 Nov 2013
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Schools: Lamar University - Class of 2011
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Is 0< a/b < 1?  [#permalink]

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13 Nov 2013, 16:17
1
3
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:07) correct 46% (02:03) wrong based on 152 sessions

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Is 0 < a/b < 1?

(1) ab> 1
(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?
Magoosh GMAT Instructor
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Posts: 4473
Re: Is 0< a/b < 1?  [#permalink]

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13 Nov 2013, 18:01
2
jenl2881 wrote:
Is 0 < a/b < 1?

(1) ab> 1
(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?

Dear jenl2881
I'm happy to help. This is a good question, and it is designed to punish folks who think of numbers only in terms of what they can count on their fingers. It's always good to have your antennae up for the whole family of numbers --- positives, negatives, zero, fractions, decimals.

Here, we have a straightforward prompt question.

Statement #1: ab> 1
Clearly, we could have a = 3 and b = 2, or a = 2 and b = 3. The first choice would produce a "no" answer to the prompt, the second a "yes" answer to the prompt. Two different answers are possible, so this statement does not lead to a definitive answer. This statement, alone and by itself, is insufficient.
I'll just mention, in passing, if ab > 1, that could meant that both numbers are positive, but it could also mean that both numbers are negatives. We didn't need that here, but we will come back to that.

Statement #2:a - b < 1
a = 2, b = 7, a - b < 1, and 0 < a/b < 1 --- an answer of "yes" to the prompt
a = 5, b = 5, a - b < 1, and a/b = 1, so it is not between 0 and 1 --- an answer of "no" to the prompt
Two different answers are possible, so this statement does not lead to a definitive answer. This statement, alone and by itself, is insufficient.

Combined:
(1) ab> 1
(2) a - b < 1

This is very tricky.
The choice a = 3 and b = 5 satisfies both statements, and a/b = 3/5 is between 0 and 1, so this produces a "yes" answer.
The choice a = 8 and b = 8 also satisfies both statements, and a/b = 8/8 = 1 is not between 0 and 1, so this produces a "no" answer.
BTW, the choice a = -7 and b = -4 would also produce a "no" answer.
Two different answers are possible, so the combined statements do not lead to a definitive answer. Everything is insufficient.

http://magoosh.com/gmat/2013/gmat-quant ... qualities/
Here's a blog about DS tips:
http://magoosh.com/gmat/2013/gmat-data- ... ency-tips/

Does all this make sense?
Mike
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Re: Is 0< a/b < 1?  [#permalink]

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13 Nov 2013, 21:11
2
jenl2881 wrote:
Is 0 < a/b < 1?

(1) ab> 1
(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?

This problem has been discussed before but I am unable to find the discussion.

You can also use your reasoning skills to get the answer here.

Is 0 < a/b < 1?
When will this happen? When a and b are both either positive or both negative. Also absolute value of a should be less than absolute value of b. We need to see if any statement gives us this info.

(1) ab> 1
This tells us that a and b have the same sign (since their product is positive). They are both either positive or both negative. But we have no info on their relative absolute values. Not sufficient.

(2) a - b < 1
This doesn't tell us whether signs of a and b are equal. So it is anyway not sufficient.
Though it does tell us that a is either less than b or slightly greater than b (less than 1 greater than b) i.e. a could be 3.9 when b is 3 but a cannot be 4 when b is 3. a can be 2 when b is 3 or it can be -4 when b is 3 etc.

Both together:
a and b have the same sign. But we don't know whether the absolute value of a is less than that of b.
a can be 3.9 when b is 3 or it can be 2.9. Not sufficient.

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Re: Is 0< a/b < 1?  [#permalink]

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13 Nov 2013, 23:59
1
jenl2881 wrote:
Is 0 < a/b < 1?

(1) ab> 1
(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?

Took me some time to do this Question . But ans is E. Here is how

From St 1 given ab>1

Let us a=3 ------> b>1/3
Now if b=3 then a/b= 1 hence given Q stem is not true
but if b=5 then a/b= 0.6 and hence given q stem is true.

So option A and D are ruled out

for St 2 we have a-b<1
if a=b=3 then a-b= 0<1 and the given stem is not true
but if b=-3 then a < - 2. If a -2.1 then a/b = -2.1/-3 =0.7 and given q stem is true.

So option B also ruled out

Combining the 2 statements, we have
ab>1 and a-b<1
ab>1 implies either both positive or both negative
Take a=b=3 then a/b=1 and Q stem not true
But if a =-4, b=-4.1 then a/b <1 and A stem is true.

Hence C ruled out, Ans has to be E
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Re: Is 0< a/b < 1?  [#permalink]

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23 Jun 2015, 21:08
1
Hi All,

In many cases, TESTing VALUES can be done with just integers. However, there will be certain questions that require that you consider non-integer possibilities and certain questions that actually have non-integer 'shortcuts' for those Test Takers who can recognize that possibility. Here, realizing that making one of your variables a non-integer can save you some serious time.

We're asked if 0 < A/B < 1. This is a YES/NO question

Fact 1: AB > 1

IF...
A = 3
B = 2.5
the answer to the question is NO

IF...
A = 2.5
B = 3
the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: A - B < 1

IF...
A = 3
B = 2.5
the answer to the question is NO

IF...
A = 2.5
B = 3
the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we already have two sets of values that fit BOTH Facts and provide different answers (one NO and one YES), so there's no more work required.
Combined, INSUFFICIENT

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Re: Is 0< a/b < 1?  [#permalink]

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23 Jun 2015, 21:33
1
jenl2881 wrote:
Is 0 < a/b < 1?

(1) ab> 1
(2) a - b < 1

Kaplan gives the answer but I am still unsure of how they got their answers. They used a = 3, b=2 and a=-3, b=-2 to test. I could use some explanation on this one. Maybe I am just over thinking it?

Hi,
lets see what does the Q stem asks us..
Is 0 < a/b < 1...
a) are both a and b of same sign?
b) is a <b?

lets see the statements now
1) stat 1 tells us that both a and b are of same sign..(a) satisfied.. nothing about (b)... insuff
2) stat 2 tells us that a is less than b+1....as a and b can be integers or fractions... nothing about relative values... insuff
combined... it just tells us both are of same sign .. nothing else... insuff
ans E
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Re: Is 0< a/b < 1?  [#permalink]

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01 Sep 2015, 05:11
We look for insufficiency in Yes/No question. If Yes and No take place at a moment, statement is INSUFFICIENT

Scenario chart:

St.1
---|a|---|b|----|ab>1|---|0<a/b<1|
----2-----5-------Y------------Y
----5-----2-------Y------------N - INSUFF
St.2
----|a|--|b|-----|a-b<1|---|0<a/b<1|
-----2----3---------Y-----------Y
-----2.5--2---------Y-----------N - INSUFF

St1+St2 (options from St2 are still fit)
----|a|---|b|----|ab>1|----|a-b<1|-----|0<a/b<1|
-----2-----3--------Y-----------Y--------------Y
-----2.5---2--------Y-----------Y--------------N - INSUFF

E
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Re: Is 0< a/b < 1?  [#permalink]

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04 Apr 2019, 08:51
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Re: Is 0< a/b < 1?   [#permalink] 04 Apr 2019, 08:51
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