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# Is ax = 6 - bx ?

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Is ax = 6 - bx ? [#permalink]

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24 Oct 2013, 17:35
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Difficulty:

45% (medium)

Question Stats:

57% (00:58) correct 43% (01:09) wrong based on 201 sessions

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Is ax = 6 - bx ?

(1) a = b
(2) 2ax = 6

GH-07.31.13 | OE to follow.
[Reveal] Spoiler: OA

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Re: Is ax = 6 - bx ? [#permalink]

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25 Oct 2013, 00:33
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Is ax = 6 - bx ?

(1) a = b. The question becomes: is ax = 6 - ax? --> is ax = 3? We don't know that. Not sufficient.

(2) 2ax = 6 --> ax=3. The question becomes: is 3 = 6 - bx? --> is bx = 3. We don't know that. Not sufficient.

(1)+(2) From (1) the question became "is ax = 3?" and (2) answers that question. Sufficient.

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Director
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Re: Is ax = 6 - bx ? [#permalink]

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29 Oct 2013, 22:16
Official Explanation

First, simplify the question:
Is ax + bx = 6 ?
Is x(a + b) = 6 ?
Either of those versions could turn out to be helpful.

Statement (1) is insufficient. We can simplify the question further:

Is ax + ax = 6 ?
Is 2ax = 6 ?
Is ax = 3 ?

Statement (2) is also insufficient. With this statement alone, we don't know anything about b, so the value of ax isn't enough.

Taken together, the statements are sufficient. Statement (1) tells us that the question is identical to:
Is 2ax = 6 ? and (2) tells us that this is true: 2ax = 6. Choice (C) is correct.

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Re: Is ax = 6 - bx ? [#permalink]

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13 Jan 2015, 16:27
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Re: Is ax = 6 - bx ? [#permalink]

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13 Jan 2015, 20:58
Hi All,

The 'algebra approach' to this DS question is pretty straight-forward (and an easy way to get to the correct answer). If you don't recognize that approach though, you can still answer this question by TESTing VALUES.

We're asked if AX = 6 - BX. This is a YES/NO question

Fact 1: A = B

IF....
X = 1
A = B = 3
Then the answer to the question is YES

IF....
X = 1
A = B = 1
Then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: 2AX = 6

Simplifying, we know that AX = 3

IF...
X = 1
A = 3
B = 3
Then the answer to the question is YES

X = 1
A = 3
B = 2
Then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
A = B
AX = 3

Since AX = 3 and A=B, we know that BX also = 3
Plugging those 'values' into the question gives us....
Is 3 = 6 - 3?
Combined, SUFFICIENT

[Reveal] Spoiler:
C

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Re: Is ax = 6 - bx ? [#permalink]

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16 Jul 2015, 09:01
1) a= b
2)2ax=6

stem 1:
a=b ; we dont know about X ; not sufficient
stem 2:
2ax=6 ; we dont know about b ; not sufficient
Clubbing stem 1 and stem2 : 2ax=6 ; ie ax= 6-ax and a=b so ax =6-bx hence C is the option

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Is ax = 6 - bx ? [#permalink]

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17 Jul 2015, 07:41
Is ax = 6 - bx ?

(1) a = b
We can rewrite the equation as ax + bx = 6 ?
Since a=b the outcome is dependent on x. Since we have no information on x, this statement is not sufficient.

(2) 2ax = 6
This means ax = 3
bx + 3 = 6 ?
We have no information on b or x so this statement is not sufficient.

Statements 1 and 2 together are sufficient.
ax + bx =6 ? : ax = 3, and a=b therefore bx = ax
3 + 3 = 6
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Is ax = 6 - bx ? [#permalink]

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19 Sep 2016, 09:51
C is correct. Here's why:

(1) a =b

NOT SUFFICIENT - we don't know what 2ax is equal to

(2) 2ax = 6

NOT SUFFICIENT - we don't know what bx is equal to

Together - (1) + (2) - We know ax = bx = 3, so 3 + 3 = 6

SUFFICIENT

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Is ax = 6 - bx ?   [#permalink] 19 Sep 2016, 09:51
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