GMAT 650+ Math Question #20 | Number Properties

GMAT Sample Questions | Face Values & Place Value | Data Sufficiency Practice

The given question is GMAT 650 level data sufficiency question testing concepts in number properties and number systems. A very interesting GMAT practice question to understand place value and face value of numbers.

Question 20: x is a two-digit positive integer. y is obtained by multiplying the tens place of x by 2. Is y > \\frac{x}{6})?

Statement 1: 20 < x < 30
Statement 2: y = 10


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Explanatory Answer | GMAT Number Properties DS

Step 1: Decode the Question Stem

Is y > \\frac{x}{6})?
We can rewrite the question as "Is 6y > 6?"

Step 2: Evaluate Statement 1 ALONE

Statement 1: 20 < x < 30
x takes values from 21 to 29.
For all these values of x, y = 2 × 2 = 4. So, 6y = 24

Approach: Counter Example
Example: x = 21, 6y is greater than x. Answer: Yes
Counter example: x = 25, 6y is not greater than x. Answer: No
Answer to the question "Is 6y > x?" is sometimes YES and sometimes NO.

We are not able to find a conclusive answer to the question using statement 1 ALONE.
Statement 1 alone is NOT Sufficient.
Eliminate answer options A and D.

Step 3: Evaluate Statement 2 ALONE

Statement 2: y = 10
So, the tens place of x is 5.
Values that x can take are 50 ≤ x ≤ 59
Because y = 10, 6y = 60
For all values of x in the range 50 ≤ x ≤ 59, 6y > x
The answer to the question "Is 6y > x?" is a conclusive YES.

We are able to answer the question a definite YES using statement 2 ALONE.
Statement 2 AlONE is Sufficient.
Eliminate answer options C and E.

Choice B is the correct answer.

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