Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #34

9

# If a and b are positive integers

If a and b are positive integers, is a/b < 9/11?

### 2 Explanations

3

Rohan Gupta

A approached the problem a bit differently.

In statement 1, it's given that a/b < 0.818
Now, 0.818 is slightly less than 9/11 (which is 0.81818181...)

So a/b is less a number that's slightly less than 9/11, so a/b < 9/11

For statement 2 : b/a > 1.223 happens to be very close to 11/9, which equals 1.222
=> b/a > 11/9
=> 9b > 11a

Which is what we need to find according to the prompt.

The solution given in the OG makes sense, however, it's bit cumbersome and there's a possibility, albeit small of an error under pressure.

Let me know how this approach seems or if there are any logical flaws here!

Aug 20, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Yes, that's correct! Great job, and thanks for sharing :D

1

JESUS J Tellez

wondering how to quickly multiply 11 *.818???

Mar 2, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Jesus :)

A quick way to multiply 11*.818 is to split up the problem:

11* .818 = (10+1)*.818
= 10*0.818 + 1*0.818

10*.818 = 8.18
1* .818 = .818

10*0.818 + 1*0.818 = 8.18 + .818
= 8.998

With that being said, it's important to recognize that we don't have to calculate anything to answer the question. Given the information, you know that you could determine the exact values to see if a/b is < 9/11. Knowing that we can answer the question is enough to say the statement is sufficient :)

This is good to keep in mind in order to save time on DS questions!

I hope this helps :D

Arthi Yerramilli

Wouldn't we still need to calculate the exact values for each scenario, given that we would have to see if we could get a solid "yes" or solid "no", but not both, for each statement? For example, wouldn't we have to double check to make sure that any number that fulfills the inequality a/b < .818 is always EITHER < or > 9/11? same for (b).

Cydney Seigerman, Magoosh Tutor

Good question!

Let's look at the two statements:

Statement 1: a/b = 0.818
Statement 2: b/a = 1.223

In each of the two statements, we're given a single value that doesn't change. In other words, we know the value of either a/b or b/a. The relationship between the value from the statement and a/b is constant and will not change. So, we can be confident that the value provided will either satisfy the inequality or not. However, there's no need to determine whether the answer is "Yes" or "No." We simply need to determine that we could determine whether the answer is "Yes" or "No" for the individual statements :)

I hope this clears up your doubts! If not, please let me know :)