Question: Value of R

Comment on Value of R

Thanks for these videos

to be honest, sometimes I just use the fact that gmat provides true information. In other words, from statement one I already know that the answer must be two --> so (6*5)/(2*1)= 15 so it seems right. Now if I have enough time I can think about it or just move on :)

This might be a risky and not valid approach but it often works. In general the information from one of the other statements often help to determine and/or verify the solution.
gmat-admin's picture

You're right in that, since the statements will never contradict each other (more on that here:, 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.

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A. 4
B. 6
C. 8
D. 10
E. 12

Please help in solving this ques.
gmat-admin's picture

Hi Prakap,

Here's my step-by-step solution:


This video just says doesnt show the steps.. :(
gmat-admin's picture

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

found the videos good and informative
gmat-admin's picture

Thanks for that!

During the 31-day month of May, a tuxedo shop rents a different number of tuxedos each day, including a store-record 55 tuxedos on May 23rd. Assuming that the shop had an unlimited inventory of tuxedos to rent, what is the maximum number of tuxedos the shop could have rented during May?


Please help me in solving this.
gmat-admin's picture

Is it safe to say that when N is odd in the combination formula there will be duplicate outcomes for every R, and when N is even there will be duplicate outcomes for every R with the exception of the middle digit?

This could be a helpful fact, especially when solving data sufficiency. For this question, I would only need to solve for R = 3 to see if the statement is sufficient.
gmat-admin's picture

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


hi brent,

I don't understand what is being asked here. Could you please explain this question to me?
gmat-admin's picture

Question link:

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?

Yes, thank you so much!

Okay I was trapped by statement 2 i thought it could be just one value
gmat-admin's picture

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

Another great video thanks Brent.
One question why do we need to calculate for 0 employee here 6C0? Is it necessary?

What's the probability of having this type of question on exam?
If the probability is high, could you provide some more links to practice? Thanks Brent.

gmat-admin's picture

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.

Get it and noted. Thanks Brent

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