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Math Expert V
Joined: 02 Sep 2009
Posts: 56260
If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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1
5 00:00

Difficulty:   45% (medium)

Question Stats: 65% (01:37) correct 35% (01:52) wrong based on 81 sessions

### HideShow timer Statistics If a, b, and c are positive, is a + b > c?

(1) a/c > b > 1

(2) ab > ac

_________________
Intern  B
Joined: 16 Jun 2018
Posts: 10
GMAT 1: 600 Q36 V37 If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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1
Bunuel wrote:
If a, b, and c are positive, is a + b > c?

(1) a/c > b > 1

(2) ab > ac

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
Senior Manager  P
Joined: 18 Jan 2018
Posts: 270
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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1
(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
Manager  G
Joined: 14 Oct 2017
Posts: 244
GMAT 1: 710 Q44 V41 If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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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.
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Intern  B
Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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Masterscorp wrote:
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.

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.
Manager  G
Joined: 14 Oct 2017
Posts: 244
GMAT 1: 710 Q44 V41 Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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rajudantuluri wrote:
Masterscorp wrote:
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.

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.

Can you please explain why the first example doesn't qualify in your opinion?
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My goal: 700 GMAT score - REACHED | My debrief - first attempt 710 (Q44,V41,IR7)

Manager  S
Joined: 07 Feb 2017
Posts: 182
Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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

Answer D. Each statement by itself is sufficient.
Intern  B
Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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Masterscorp wrote:
rajudantuluri wrote:
Masterscorp wrote:
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.

As stated before we must choose examples where a>c but the values you’ve chosen for a and c are 2, 3 respectively.
So it doesn’t meet the criteria.

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.

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

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
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Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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

(1) a/c > b > 1

(2) ab > ac

(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.

Manager  B
Joined: 22 Sep 2017
Posts: 168
If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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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[/quote]

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.
Intern  B
Joined: 16 Jun 2018
Posts: 10
GMAT 1: 600 Q36 V37 ### Show Tags

Hi,

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.

Attachments doubt 2.png [ 148.67 KiB | Viewed 702 times ]

ISB School Moderator G
Joined: 08 Dec 2013
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Concentration: Nonprofit, Sustainability
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Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac  [#permalink]

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

(1) a/c > b > 1

(2) ab > ac

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.
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I never gave up what I wanted- Re: If a, b, and c are positive, is a + b > c? (1) a/c > b > 1 (2) ab > ac   [#permalink] 26 Jun 2019, 22:40
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