If a b 0, is b 1/2 (2) 1/a + 1/b = 1

Question

If a > b > 0, is b < 2?

(1) 1/a > 1/2
(2) 1/a + 1/b = 1

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Pallavimalik2597 · Answer

It is given in the question that both the number are +ve because a>b>0

Question is to find out whether b<2 or not, answer should be in Yes/No

1. 1/a>1/2
Since a is +ve we can multiply both the sides by a
1>a/2
Now multiply above equation by 2
2>a

We can rewrite it as a<2 which means b is also less than 2

A is sufficient

2. 1/a+1/b=1
Which means
(A+b)/ab=1
(a+b)=ab

It is only possible if a and b are 2 or 0
Both the numbers can’t be 0 as it is given that a,b are greater than 0

Hence a,b=2
We can see b is not less than 2 but equal 2
This stament is also sufficient for us to find the answer

Hence answer is D

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Mirko92 · Answer

Regarding statement 2, aren't a and b supposed to be different numbers because a>b? So they shouldn't both be 2 right?

agrasan · Answer

A quick question on the answer:

It is not given that a and b are integers only, 
For statement-2, a can also be 3 and b can be 3/2 which gives 1/a + 1/b = 1, this also supports a>b and b<2, this will make statement 2 as insufficient due to multiple solutions of b = 2, 3/2.

Please let me know if I missed anything important here.

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N^2 · Answer

Let's contribute my first two cents to the GMAT forum:

(I)
1/a>1/2 (multiplying each term by (-1)),
a<2.
If a <2, then b should also be less than 2 because b<a. Sufficient

(II)
1/a+1/b=1
1/b=1-1/a
1/b=(a-1)/a
b= a/a-1. Also, it is know that a>0
Evaluating possible solutions to the equation:
1) If 0<a<1 --> a-1<0
b=a/(a-1)=(positive number)/(negative number)=negative number. This is not acceptable because b>0. Case not considered.
2) If a=1 --> a-1=0
b=a/(a-1) = 1/0. This is not acceptable due to division by 0 is undefined. Case not considered.
3) If 1<a<2 --> 0<a-1<1--> undefined>1/(a-1)>1--->undefined>a/(a-1)>2
This is not acceptable because b>2>a contradicts the premise a>b>0. Case not considered.
4) If a=2 --> a-1=1
b=a/(a-1) = 2/1=2. This is not acceptable because b=a=2 contradicts the premise a>b>0. Case not considered.
5) If a>2 --> a-1>1 -->1<b=a/(a-1)<2
Every number divided by its preceding number is less than 2 and greater than 1, for example: 3/2=1.5, 4/3 = 1.33, 5/4=1.25 and so on. The same rules apply to non-integers numbers, for example (=1)1.5/1.5<2.5/1.5<3/1.5(=2).
Therefore, the only possible solution is case 5 when a>b>0 and b>2. Suficient

Answer D

If a > b > 0, is b < 2? (1) 1/a > 1/2 (2) 1/a + 1/b = 1

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