Digit DS Question.

Hi kamalakarthi,

If you're really comfortable with "decimal shift" math, then you might be able to think your way past this question without doing much work. However, for this type of question, you'll find it helpful to TEST VALUES, use the results to spot patterns and PROVE what the answer is.

We're asked if the HUNDREDTHS digit of D is > 5. This is a YES/NO question.

Before we get into the prompt, I'm going to review a little math vocabulary:

123.4567

The 4 is the TENTHS digit
The 5 is the HUNDREDTHS digit
The 6 is the THOUSANDTHS digit
The 7 is the TEN-THOUSANDTHS digit

Fact 1: The TENTHS DIGIT OF 10D IS 7

If D = .17, then 10D = 1.7 (so the tenths digit is 7). In this test, the HUNDREDTHS digit of D is 7, so the answer to the question is YES.
If D = .27, then 10D = 2.7 (so the tenths digit is 7). In this test, the HUNDREDTHS digit of D is 7, so the answer to the question is YES.
As long as you following the "restriction" in Fact 1, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: The THOUSANDTHS digit of D/10 is 7
If D = .17, then D/10 = .017 (so the thousandths digit is 7). In this test, the HUNDREDTHS digit of D is 7, so the answer to the question is YES.
If D = .27, then D/10 = .027 (so the thousandths digit is 7). In this test, the HUNDREDTHS digit of D is 7, so the answer to the question is YES.
This is essentially the same pattern as in Fact 1, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

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

Here's a similar question to practice with: https://www.beatthegmat.com/hundredth-digit-t280191.html

Cheers,
Brent

Hi j_shreyans,

The definition of each of the decimal spots is based on how the decimal would look as a fraction.

For example:

.1 = 1/10 = a tenth, so in the number 123.4567, the 4 is called the TENTHS digit.

.01 = 1/100 = a hundredth, so the 5 is called the HUNDREDTHS digit.

Etc.

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