Question: Value of R

You're right in that, since the statements will never contradict each other (more on that here: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1104), the conclusion we reach after one statement can help with the other statement. However, we need to be absolutely certain that we determine the sufficiency of the second statement SOLELY ON ITS OWN.

Hi Prakap,

Here's my step-by-step solution: https://gmatclub.com/forum/a-certain-square-is-to-be-drawn-on-a-coordina...

Cheers,
Brent

Sorry, but I'm not sure what you're referring to. Can you please elaborate?

Thanks for that!

Here's my full solution: https://gmatclub.com/forum/during-the-31-day-month-of-may-a-tuxedo-shop-...

Cheers,
Brent

You're absolutely correct about that property.

In general, nCr = nC(n-r)

Some examples:
10C3 = 10C7
8C2 = 8C6
5C1 = 5C4

If n is ODD, then each outcome will be duplicated.
For example:
7C0 = 1
7C1 = 7
7C2 = 21
7C3 = 35
7C4 = 35
7C5 = 21
7C6 = 7
7C7 = 1

If n is EVEN, then each outcome will be duplicated EXCEPT for the middle outcome.
For example:
6C0 = 1
6C1 = 6
6C2 = 15
6C3 = 20
6C4 = 15
6C5 = 6
6C6 = 1

Cheers,
Brent

Question link: https://gmatclub.com/forum/the-difference-942-249-is-a-positive-multiple...

The difference 942 − 249 is a positive multiple of 7. If a, b, and c are nonzero digits, how many 3-digit numbers abc are possible such that the difference abc − cba is a positive multiple of 7 ?

A. 142
B. 71
C. 99
D. 20
E. 18

The question starts with an example.
Notice that the digits in 249 are the same as the digits in 942, except in REVERSE ORDER.
We're told the difference 942 - 249 is a positive multiple of 7.
In other words, 693 is a multiple of 7, which is true since 7 x 99 = 693.

It's important to note that not all 3-digit numbers share the same property.
For example, 621 - 126 = 495, and 495 is NOT a positive multiple of 7
Likewise, 765 - 567 = 198, and 198 is NOT a positive multiple of 7
CONVERSELY, 851 - 158 = 693, and 693 IS a positive multiple of 7.

So, the property applies to some 3-digit numbers, and doesn't apply to other 3-digit numbers.
The question asks us to determine just how many 3-digit numbers (with non-zero digits) are such that abc − cba is a positive multiple of 7

Does that help?

A lot of students will fall for that trap.
The key property here is that nCk = nC(n-k)
For example: 7C2 = 7C5 and 11C3 = 11C8

I thought it would be worthwhile to include 6C0 in my solution mainly so that students can see the symmetric nature of combinations.
For the purposes of preparing for the GMAT, the main takeaway here is that 6C0 = 1, since many students feel this should equal 0.