Data Sufficiency

NandishSS wrote: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

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

NandishSS wrote: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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