Is 0

Question

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?

mikemcgarry · Answer

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 . Answer = (E) Here's a blog about inequalities: https://magoosh.com/gmat/2013/gmat-quant ... qualities/ Here's a blog about DS tips: https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/ Does all this make sense? Mike :-)

KarishmaB · Answer

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.

Answer (E)

WoundedTiger · Answer

Took me some time to do this Question :evil:

. 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

EMPOWERgmatRichC · Answer

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

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

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

Temurkhon · Answer

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|---|01|----|a-b<1|-----|0

exc4libur · Answer

(1) ab> 1: insufic. (a,b)=(-4,-2)…ab=8>1…a/b=-4/-2…answer:no (a,b)=(1,3)…ab=3>1…a/b=1/3…answer:yes (2) a - b < 1: insufic. (a,b)=(-4,-2)…a-b=-2<1…a/b=-4/-2…answer:no (a,b)=(1,3)…a-b=-2<1…a/b=1/3…answer:yes (1&2): insufic. (a,b)=(-4,-2)…a-b=-2<1…ab=8>1…a/b=-4/-2…answer:no (a,b)=(1,3)…a-b=-2<1…ab=3>1…a/b=1/3…answer:yes Answer (E)

bumpbot · Answer

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Is 0< a/b < 1?

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