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If a is less than 80% of b, is a less than 50? (1) b a = 20

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If a is less than 80% of b, is a less than 50? (1) b a = 20 [#permalink] New post 20 Jun 2011, 19:44
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If a is less than 80% of b, is a less than 50?

(1) b – a = 20

(2) b < 50
[Reveal] Spoiler: OA
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Re: A DS On % [#permalink] New post 20 Jun 2011, 21:30
a < 0.8b, so is a < 50

(1) b – a = 20
b = a + 20

=> a < 0.8(a+20)

=> 0.2a < 16

=> a < 80

Not Sufficient as a can be 79 or 0


(2) b < 50


If b < 50, then 0.8b < 0.8 * 50

=> 0.8b < 40

Now a < 0.8b

=> a < 40 and a < 50

So Sufficient

Answer - B
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If a is less than 80% of b, is a less than 50? [#permalink] New post 24 Aug 2013, 04:39
If a is less than 80% of b, is a less than 50?

(1) b – a = 20

(2) b < 50
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Re: If a is less than 80% of b, is a less than 50? [#permalink] New post 24 Aug 2013, 04:51
Stiv wrote:
If a is less than 80% of b, is a less than 50?

(1) b – a = 20

(2) b < 50


Statement 1
b-a = 20
b- .80b (min)=20
Max(0.20b)=20
b (max)=100

Now we that the max value of b is 100, but we still don't know the value of a
if a =.7b , then answer is yes
if a =.1b , then answer is No
Thus Insufficient

Statement 2
b<50
In this case even if we take the best possible scenario we see that a is less than 50
b=50
a=.8b = 40
The answer is NO
Thus Sufficient

Answer B
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Re: If a is less than 80% of b, is a less than 50? [#permalink] New post 24 Aug 2013, 05:04
Stiv wrote:
If a is less than 80% of b, is a less than 50?

(1) b – a = 20

(2) b < 50


since a is 80 % of b means a<b
now clearly from statement 2 we know b<50...hence a <50..sufficient

now statement 1 = > b=a+20...and a=0.8b
so here it clearly depends on value of b ....hence insufficient

hence B
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Re: If a is less than 80% of b, is a less than 50? [#permalink] New post 25 Aug 2013, 06:26
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Re: If a is less than 80% of b, is a less than 50? (1) b a = 20 [#permalink] New post 22 Oct 2013, 04:26
I just kind of plugged in numbers.

b=120, a =100 so I is not sufficient
if b<50 and a is less than 80% of it, it has to be less than 50 too.
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Re: If a is less than 80% of b, is a less than 50? (1) b a = 20 [#permalink] New post 22 Oct 2013, 05:27
Statement 1
Case 1 : let b = 100,
b - a = 20,
100 - a = 20
a = 80 (80 is more than 50) (case 1 is No)

Case 2: let b = 50
b - a = 20
50 - a = 20
a = 30 ( this is less than 50, case 2 is YES)

So, this is insufficient

Statement 2

Given: b < 50
let b = 49
b - a = 20
49 - a = 20
a = 29

80% or 4/5 of b will always be less than 49. No need to calculate. This statement is sufficient. Ans: B
Re: If a is less than 80% of b, is a less than 50? (1) b a = 20   [#permalink] 22 Oct 2013, 05:27
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