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If a>2, is b<1?

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Joined: 22 Mar 2017
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Updated on: 07 Jun 2017, 19:58
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If a>2, is b<1?

(1) a·b<2

(2) a·b>0

Originally posted by Nathanlambson on 07 Jun 2017, 14:31.
Last edited by Bunuel on 07 Jun 2017, 19:58, edited 1 time in total.
Renamed the topic.
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Re: If a>2, is b<1?  [#permalink]

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07 Jun 2017, 18:15
Nathanlambson wrote:
If a>2, is b<1?

(1) a·b<2

(2) a·b>0

(1) if a= 2.1
then b < 1
if a =3 then b<1
as a>2 then fraction 2/a is always<1

suff

(2) b is independent of a and can be any value >0
it may be 0.5 when a= 10 then b< 1----YES
or may be b=2 when a = 3 or any integer ...b>1 .-----NO

insuff

Ans A
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Re: If a>2, is b<1?  [#permalink]

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08 Jun 2017, 08:07
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Nathanlambson wrote:
If a>2, is b<1?

(1) ab < 2

(2) ab>0

Target question: Is b < 1?

Given: a > 2

Statement 1: ab < 2
Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a.
When we do this we get: b < 2/a
Since a > 2, we know that the fraction's denominator is greater its numerator, which means 2/a must be less than 1
So, 2/a < 1
Since b < 2/a, we get: b < 2/a < 1
In other words, b < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ab > 0
Let's TEST some numbers.
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 3 and b = 2, in which case b > 1
Case b: a = 3 and b = 0.1, in which case b < 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: If a>2, is b<1?  [#permalink]

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08 Jun 2017, 08:14
(1) is sufficient

If a >2
Then a.b<2 is possible only when b<1

(2) is not sufficient
If a>2 and
a.b>0
Using two values of b
b=1/2 and b=3/2

a.b>0 stands for both the values and hence not sufficient

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Re: If a>2, is b<1?  [#permalink]

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10 Jun 2017, 22:11
statement1:
a-b<2
b>a-2
b>=3-2 (as a>2)
b>=1 sufficient

statement2:
a-b>0
b<a
b<=3 (as a>2)
not sufficient
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Re: If a>2, is b<1?  [#permalink]

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06 Jul 2017, 16:07
Nathanlambson wrote:
If a>2, is b<1?

(1) a·b<2

(2) a·b>0

We are given that a > 2 and need to determine whether b < 1.

Statement One Alone:

a·b < 2

Let’s divide each side by a. Note that since a > 2, a is positive, and so the inequality sign will not be reversed:

b < 2/a

2/a is a fraction in which the denominator is greater than the numerator. Thus, 2/a < 1 and b < 2/a < 1.
Statement one is sufficient to answer the question.

Statement Two Alone:

a·b > 0

The information in statement two is not sufficient to answer the question. For example, if a = 3 and b = 1/2, then b is less than 1; however, if a = 3 and b = 3, then b is not less than 1.

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Re: If a>2, is b<1?  [#permalink]

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19 Oct 2017, 12:44
GMATPrepNow wrote:
Nathanlambson wrote:
If a>2, is b<1?

Statement 1: ab < 2
Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a.
When we do this we get: b < 2/a
Since a > 2, we know that the fraction's denominator is greater its numerator, which means 2/a must be less than 1
So, 2/a < 1
Since b < 2/a, we get: b < 2/a < 1
In other words, b < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Hi Brent,

Can we not use a similar approach on Statement 2?

Statement 2: ab > 0
Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a.
When we do this we get: b > 0

Since we cannot answer the target question with certainty, statement 2 is INSUFFICIENT
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Re: If a>2, is b<1?  [#permalink]

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21 Sep 2019, 08:05
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Re: If a>2, is b<1?   [#permalink] 21 Sep 2019, 08:05
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