gmat_winter wrote:Is the number x between 0.1 and 1.0?

(1) 420x is less than 168.
(2) 650x is greater than 130.

OAC

Target question: Is x between 0.1 and 1.0?

Statement 1: 420x is less than 168.
So, 420x < 168
Divide both sides by 420 to get: x < 168/420
Simplify to get: x < 0.4
There are several values of x that satisfy this condition. Here are two:
Case a: x = 0.2, in which case x IS between 0.1 and 1
Case b: x = -5, in which case x is NOT between 0.1 and 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 650x is greater than 130.
So, 650x < 130
Divide both sides by 650 to get: x > 130/650
Simplify to get: x > 0.2
There are several values of x that satisfy this condition. Here are two:
Case a: x = 0.3, in which case x IS between 0.1 and 1
Case b: x = 5, in which case x is NOT between 0.1 and 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that x < 0.4
Statement 2 says that x > 0.2. In other words, 0.2 < x
Combine to get 0.2 < x < 0.4
If x is between 0.2 and 0.4, then we can be certain that x is between 0.1 and 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Hi gmat_winter,

In this DS prompt, you can actually avoid almost all of the "math" entirely. The 'design' of the prompt rewards Test Takers with 'pattern-matching' ability, and a variation on TESTing VALUES will work nicely here.

We're asked if X is between 0.1 and 1.0. This is a YES/NO question.

Fact 1: 420X is less than 168.

420X < 168

X < 168/420

168/420 is clearly a POSITIVE FRACTION that is bigger than .1 (10% of 420 = 42, so 42/420 would be .1)

IF X is close to 168/420, then the answer to the question is YES
If X is 0, then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: 650X is greater than 130

650X > 130

X > 130/650

130/650 is clearly a POSITIVE FRACTION that is bigger than .1 (since 65/650 = .1).

IF X is close to 130/650, then the answer to the question is YES
If X is 1, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that....

168/420 > X > 130/650

X is clearly a POSITIVE FRACTION that is greater than .1 (since 65/650 = .1)
The answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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