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# Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?

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Math Expert
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Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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23 Sep 2015, 02:29
1
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65% (hard)

Question Stats:

53% (02:01) correct 47% (02:00) wrong based on 147 sessions

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Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?

(1) B > 0

(2) A < C

Kudos for a correct solution.

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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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Updated on: 23 Sep 2015, 13:06
2
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

Kudos for a correct solution.

Solution: For problems such as this, it is sometimes better to simplify the question.
(A + B) / (C + B) > A/C --->(1)
Subtract 1 on both sides.
==> (A - C) / (C + B) > (A - C)/C .Numerators are same .
If A = C , then then (1) is always true.
Else, for this to be true C+B<C ==>B<0.
So we have find whether B<0.

Statement1 : B>0. But we dont know whether a=c. Insufficient

Statement2 : It says nothing about B. Insufficient.

Combined : A != C and B>0. No. Sufficient.
Option C

Originally posted by anudeep133 on 23 Sep 2015, 03:47.
Last edited by anudeep133 on 23 Sep 2015, 13:06, edited 1 time in total.
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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23 Sep 2015, 12:20
3
@anudeep123:

A is wrong. what if a=b=c=1? Combining both, the left side is always going to be greater than A/C by 1. Correct answer is C.
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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24 Sep 2015, 02:57
2
Since we are told that A and C are both greater than zero, that means we can freely multiply and divide these two variables in the inequality but not B since we aren't told if B is positive or negative.

With that in mind, lets play around with the question first.
(A+B) A
------- > ---
(C+B) C

Since we can multiply/divide A and C around the inequality lets cross multiply

AC + AB > AC + BC

Subtract AC on both sides and we're left with "is AB > BC"

Now on to the choices

1) B>0
Insufficient since this doesn't tell us anything about C and A.

2) A<C
Again, insufficient since if you consider this statement alone, we aren't told anything about the value of B. If B is positive then BC will be be greater than AB if C > A. However, if B is a negative value then BC will be less than AB if C > A

1) and 2)
Sufficient. We know B is positive. This fills the gap in the second statement. If B is positive then having C > A ensure that BC > AB

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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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24 Sep 2015, 20:18
Additions of B in numerator and denominator can be tricky,

I guess answer should be E
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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24 Sep 2015, 21:24
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

st1 -- B is positive given
also A and C are positive

hence (A + B) / (C + B) > A/C

We can cross multiply

AC + BC > AC + AB
BC > AB
BC - AB > 0
B( C-A) >0

already that B is >0 hence --- C >A

Therefore ---- We got the relation between c and a .

Now

(A + B) / (C + B) > A/C Use number any positve number that satisfy C>A and B is also positive .We will get a definitive ans .

ST B . Not sufficient . NO clues given for B

Hence Ans is A .
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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05 Oct 2015, 01:39
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

For (1), we are only given that b is a positive number. Picking values is a good strategy here. If we can choose values such that we get a “yes” and choose values so that we get a “no” then we can quickly eliminate. If a = 1 and c = 1 and b = 1, then the inequality is NOT correct. However, if a = 1 and c = 2, and b = 3, we get 4/5 > 1/2, which IS correct. (2) can be proved insufficient similarly. Combined, if b is positive and a < c, then it will continue to INCREASE the left-hand side of the inequality no matter what values we pick.

Remember, even the most seemingly complex Data Sufficiency questions can be overcome with solid strategy!
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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28 Apr 2016, 18:03
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

Kudos for a correct solution.

I solved it by remembering that if 0 < x/y < 1, then adding same positive number to the numerator and denominator, the value will increase.

1. B>0
just listed 2 possible options
A=C
B=2
A+2/C+2 = A/C so equal

A=3
C=5
B=1
3+1/5+1 = 4/6 = 2/3 > 3/5

2 outcomes, A alone is not sufficient.

2. A<C
ok, so 0<A/C<1 but what about B? if B is negative, then adding it to numerator and denominator would decrease the new fraction.
clearly 2 alone is not sufficient.

1+2
A<C
and B>0
sufficient.
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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28 Apr 2016, 23:22
1
whenever we add something to numerator and denominator, percentages come into play! like if the percentage increase in Numerator is more than the percentage increase in denominator, ratio increases and vice versa.

So here we are adding a number B to numerator (A) and denominator (C) but we don't know which one is larger so as know whose percentage increase is more.

St1: B>0 now we know that we are adding a number and not subtracting since B is positive but we don't know whether A >C or C>B so we can't comment on the change in ratio.

St2: A<C but this does not tell about B( whether we are subtracting a number or adding a number)

1 & 2 combined: now B>0 so we are adding something. and A<C so percentage change in numerator(A) would be more as compared to percentage change in denominator(C) . So the ratio will increase.

Hence C.

Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

Kudos for a correct solution.
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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29 Jun 2016, 03:58
The first temptation is to cross-multiply the expressions, but we can't do it because we only know that A, C are positive, but we don't know the sign of B.
So for start let the question stem as it is.

from 1) $$b>0$$ Now we know all the signs and we can cross multiply. We get:

$$CA+CB>CA+AB$$
CA+CB>CA+AB
$$CB>AB$$
$$CB-AB>0$$
$$B(C-A)>0$$
Now we have that B multiplied by (C-A) is positive. How can that be? only if B>0 and (C-A)>0 or B<0 and (C-A)<0

From the stem we are told that B>0, so the question becomes "Is (C-A) positive?" From 1) we can't extract any info on C-A so it's insufficient.

from 2) A<C, so 0<C-A We don't know the sign of B, so we can't cross-multiply and that impairs us from working on the question. Insufficient.

1) + 2) from 1 we got our rephrased question, "Is (C-A) positive?" and from 2) we get that A<C, so 0<C-A and we now have enough info to answer.
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?  [#permalink]

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09 Apr 2018, 10:41
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Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?   [#permalink] 09 Apr 2018, 10:41
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