Is ab = 9c^2–4?

Question

Is ab = 9c^2–4?

(1) a divided by 3 is equal to c with a remainder of 2.
(2) b divided by 3 is equal to c minus 2/3.

Kudos for a correct  solution .

Cadaver · Answer

C - Using A & B....A= 3c+2, B= 3c-2

buddyisraelgmat · Answer

Ans C

Stmnt 1 -Nothing about b - Not Suff
Stmnt 2 - Nothing about a - Not Suff

Combining, a = 3c + 6 and b = 3c - 2
Possible to compute and answer the Question - Hence Suff !

Ans - C

aj13783 · Answer

1. a = 3c+6
2. b = 3c-2

therefore ab = (3c+6)*(3c-2) = 9C^2+12C-12 <> 9C^2 - 4

Option C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Solution: C

Statement (1) says nothing about b; INSUFFICIENT. Statement (2) says nothing about a; INSUFFICIENT. When combining the statements, be sure to simplify them first. If a/3 = c with a remainder of 2, then a = 3c + 2. If b/3 = c – 2/3, then b = 3c-2. Thus ab = (3c+2)(3c-2), or 9c^2–4; (C).

EMPOWERgmatRichC · Answer

Hi buddyisraelgmat and aj13783,

While you both selected the correct answer, you both made the same "math mistake" in your work. While that error didn't hurt you on this question, it might impact other questions in the future, so it's worth 'fixing.'

In Fact 1, we're told that when A is divided by 3 equals C with a remainder of 2. This translates into:

A/3 = C remainder 2

If you want to isolate the A, then you multiply both sides by 3, BUT you do NOT multiply the remainder (since the remainder represents the "leftover pieces" and that part does NOT get tripled).

So

A = 3C + 2 (not A = 3C + 6)

Here is an example of that, using real numbers.....

Let's say A = 14

14/3 = 4 remainder 2

14 = 3(4) + 2

GMAT assassins aren't born, they're made,
Rich

ajxxatic · Answer

Hi,
I understand that a = 3c+2 but how is B = 3c-2? B leaves a remainder of -2/3. Please double check.

Bunuel · Answer

(2) b divided by 3 is equal to c minus 2/3.

b/3 = c - 2/3;

Multiply by 3: b = 3c - 2.

Hope it's clear.

Nunuboy1994 · Answer

Before looking at the statements we can easily see that this question is just a variation of (a+b)(a-b) - a common theme on the GMAT- (3b-2)(3b +2)

Statement 1

If a/3 = c remainder 2 then = a= 3c +2

but no info about "b" insuff

Statement 2

Same thing

b/3= c-2/3 - use algebra
b= 3c- 2

no info about

a

St 1 & 2

(3c-2)(3c +2) suff

c

fearinyoureye · Answer

Sorry but I don't understand how a/3 = c + 2 is equal to 3c + 2... Shouldn't it be 3c+6?

EMPOWERgmatRichC · Answer

Hi fearinyoureye,

The question you're asking is reasonable based on how the information is 'presented' - but it's worth noting that we're dealing with a REMAINDER - and not simply an algebraic equation. Here's what that means:

In Fact 1, we're told that A divided by 3 equals C with a remainder of 2. This translates into:

A/3 = C remainder 2

The poster you're referring to wrote "C remainder 2" as "C + 2", which is fine, but you still have to remember that it's a REMAINDER.

If you want to isolate the A, then you multiply both sides by 3, BUT you do NOT multiply the remainder (since the remainder represents the "leftover pieces" and that part does NOT get tripled).

So

A = 3C + 2 (not A = 3C + 6)

Here is an example of that, using real numbers.....

Let's say A = 14

14/3 = 4 remainder 2

14 = 3(4) + 2

Notice how we ONLY multiply the '4' and NOT the '2' (since the remainder is not something that's being tripled - it's the 'leftover piece').

GMAT assassins aren't born, they're made,
Rich

fearinyoureye · Answer

That makes a lot of sense, thank you!

nsdl1985 · Answer

then why we are not applying the same logic to b?

bumpbot · Answer

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Is ab = 9c^2–4?

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Is ab = 9c^2–4?

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