Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine whether the positive two-digit integer N is less than 40.
Statement One Alone:
The units digit of N is 6 more than the tens digit.
With the information in statement one, we know the units digit is the larger of the two digits in N. So let’s say the units digit is 9 (the largest digit possible); then the tens digit will be 3 (since 9 is 6 more than 3). Thus this makes N = 39, which is less than 40. Now let’s say the units digit is 8; then the tens digit will be 2 and thus N = 28, which is still less than 40. Let’s say the units digit is 7; then the tens digit will be 1 and thus N = 17, which is again less than 40. At this point, we can’t make the units digits any smaller; if we did, the tens digits would be 0 or negative, but we know N is a positive two-digit integer.
Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
N is 4 less than 4 times the units digit.
Again, let’s test some possible numerical values for the units digit. Let’s start with 9 again since it’s the largest digit possible. If the units digit is 9, then N = 4(9) – 4 = 32, which is less than 40. If the units digit is any smaller, then N will be less than 32, which means N will always be less than 40. If you can’t see this, look at the following:
If the units digit is 8, then N = 4(8) – 4 = 28.
If the units digit is 7, then N = 4(7) – 4 = 24, etc.
Statement two is also sufficient to answer the question.
Answer: D
