Does 8x = 16 + 2x ?

[NandishSS]

Does 8x = 16 + 2x ?

(1) -3x is greater than or equal to -9
(2) 2x is greater than or equal to 6

OA:B

Source:800Source

[Brent@GMATPrepNow]

Does 8x = 16 + 2x ?

(1) -3x is greater than or equal to -9
(2) 2x is greater than or equal to 6

Target question: Does 8x = 16 + 2x ?
This is a good candidate for rephrasing the target question.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take: 8x = 16 + 2x
Subtract 2x from both sides to get: 6x = 16
Divide both sides by 6 to get: x = 16/6 = 8/3 = 2 2/3

REPHRASED target question: Does x = 2 2/3?

Statement 1: -3x is greater than or equal to -9
In other words, -3x ≥ -9
Divide both sides by -3 to get: x ≤ 3 [we flipped the direction of the inequality since we divided both sides by a NEGATIVE value]
There are several values of x that satisfy the condition that x ≤ 3.
So, x COULD equal 2 2/3 or x MIGHT NOT equal 2 2/3
Since we cannot answer the REPHRASE target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2x is greater than or equal to 6
In other words, 2x ≥ 6
Divide both sides by 2 to get: x ≥ 3
If x is GREATER than or equal to 3, then x can NEVER equal 2 2/3
In other words, the answer to our REPHRASED target questions is NO, x does not equal 2 2/3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

[[email protected]]

Hi NandishSS,

Several of the DS questions that you've face on Test Day will be easier to deal with if you 'simplify' the given question.

Here, we're asked if 8X = 16 + 2X? You can combine like terms in this question and simplify...

8X = 16 + 2X
6X = 16
3X = 8

Now we can answer the question "does 3X = 8?" This is a YES/NO question.

1) -3X is greater than or equal to -9

This Fact tells us that -3X >= - 9

We can multiply both sides by -1/3.....

X <= 3

IF....
X = 8/3, then the answer to the question is YES.
X = 2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) 2x is greater than or equal to 6

Again, we can simplify the given Fact...

2X >= 6
X >= 3

With this information, we know that 3X will always be AT LEAST 9, so the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

Final Answer: B

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

[Jay@ManhattanReview]

Does 8x = 16 + 2x ?

(1) -3x is greater than or equal to -9
(2) 2x is greater than or equal to 6

OA:B

Source:800Source

The equation: 8x = 16 + 2x can be manipulated to x = 8/3 = 2.67. So the rephrased question is: Does x = 2.67?

S1: We can write the statement as -3x ≥ -9. After multiplying the inequality by '-1', we get

=> 3x ≤ 9 [note the sign chnage]

=> x ≤ 3 => x can be any number less than equal to 3 (integers, fraction, decimals, 0, negative). It can even be 2.67. If yes, the answer is YES, else NO. No unique answer.

S2: We can write the statement as 2x ≥ 6

=> x ≥ 3 => x can be any number greater than equal to 3 (integers, fraction, decimals: all positive). It cannot be 2.67. The answer is YES. A unique answer. Sufficient.

OA: B

-Jay
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