If a, b, and c are positive, is a + b c? (1) a/c b 1 (2) ab ac

Question

If a, b, and c are positive, is a + b > c?

(1) a/c > b > 1

(2) ab > ac

mrinalsharma1990 · Answer

Option 1
Since a/c>b a is>c hence a+b>c- sufficient

Option 2
ab>ac which means b>c hence a+b>c- sufficient

Ans- D

baru · Answer

(1) a/c > b > 1
 => a>bc>c 
 => a>c
 => a + ( some thing positive) is always > c ==> Sufficient

(2) ab > ac
 if we consider some fractions here it will fail .
 a = 1/4 , b = 3/4 , c = 1 ==> No
 a = 2 , b = 3 , c = 1 ==> Yes ====> Insufficient

Option A

Masterscorp · Answer

B imo.

1)   gives us a>bc but this is not sufficent to answer the question. If a=2, b= \frac{1}{2}  and c=3 we get 2> \frac{3}{2} . If we plug in the same values in the equation from the stem we receive:

2+ \frac{1}{2} <3. This means that the inital statement would be incorrect. 
However, if we choose a=6, b=3 and c=1 and plug those values into the initial statement we receive:

6+3>9. This means that the initial statement would be correct.
In conclusion, statement 1 is  not sufficent .

2)  can be converted to a>c so a+b>c will always be true. Hence, this statement is sufficient.

rajudantuluri · Answer

I think the first example doesn't qualify here.

Since all the numbers are positive, the first expression can be written as

a>bc>c

This implies that a>c. The first example that you chose doesn't meet this criteria. If you try examples where a>c then you will see that this is always sufficient.

Masterscorp · Answer

Can you please explain why the first example doesn't qualify in your opinion?

gmatzpractice · Answer

Since all are positive: 
(1) a/c > 1; a > c 
(1) b > c

Answer D. Each statement by itself is sufficient.

rajudantuluri · Answer

As stated before, you need to choose values for a and c such that a is greater than c. You’ve chosen 2 and 3 respectively for a and c so it doesn’t meet the criteria

amanvermagmat · Answer

(1) Since a/c > 1 and both a/c are positive, we can write a > c. Now b is a positive number, so adding b to a will further increase the value of a. So definitely a+b > c. Sufficient.

(2) ab > ac. Since a is positive we can divide both sides by a to get b > c. Now a is a positive number, so adding a to be will further increase the value of b. So definitely a+b > c. Sufficient.

Hence  D answer

jackspire · Answer

Hello, @baru

(1) a/c > b > 1
 => a>bc>c 
 => a>c
 => a + ( some thing positive) is always > c ==> Sufficient

(2) ab > ac
 if we consider some fractions here it will fail .
 a = 1/4 , b = 3/4 , c = 1 ==> No
 a = 2 , b = 3 , c = 1 ==> Yes ====> Insufficient

Option A

When we take statement-2:
ab>ac
if we omit the common item "a", then we get
b>c
As per your reasoning of the first option,
b + something(i.e. a) will always be greater than "c".

So, we can find a solution from both the options. And the answer is D.
Hope it helps.

mrinalsharma1990 · Answer

Hi,

I have a doubt with the question below, please help:

Please refer to the attached screenshot. As per me the answer should be -8, however the answer as per the solution offered for this question is -800.

Please help me understand where I am going wrong.

Thanks in advance.

LeoN88 · Answer

Start with Easy Statement 2. b>c, as a>0 now definitely b+a>c if b>c. Sufficient. Statement 1. 1 < b < a/c Let's try to satisfy a + b > c 1 < 2 < 7/2, Okay. Now Let's try to negate a + b > c, or satisfy c>a+b 1 < 2 < a/5, a has to be more than 10, not possible. So, 1 < b < a/c tells us a + b > c is the only possible inference. D. Each statement independently sufficient.

If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac

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