Question: Socks

Comment on Socks

What are the question should I try from official gmat 2016 book for probability . Thank you
gmat-admin's picture

You'll find the answer to that question at the bottom of

Hey, thanks for the videos, you've been a great help.

For this question, considering statement 2, if we solve the equation for W, which is W^2 - W - 12 > 0, I get the following 2 results:

W > -3
W > 4

Now if we use W>4, we can arrive the answer that the statement is sufficient. My question is that can we disregard W > -3? By this equation, W can also be 1,2,3...and so on. Please explain
gmat-admin's picture

Be careful.

When we solve the inequality W^2 - W - 12 > 0, we get first get (W - 4)(W + 3) > 0

When we solve, we get: W > 4 or W < -3 (less than -3, not greater than -3)
For more on solving quadratic inequalities, watch:

If W < -3, then some possible values of W are -4, -5, -6, -7, etc.
None of these values fit the requirement that W must be an integer that's greater than or equal to zero.

Poorly written question, because it doesn't say the socks are ONLY black and white.

Be careful.
gmat-admin's picture

That's intentional. We don't need the proviso that the socks are black and white only. In fact, there's no reason why there can't be socks of other colors, but it doesn't change the answer.

Its a very good question. can you please scale how hard this question could be on GMAT?
gmat-admin's picture

I'd say that it's a 700+ level question.

1Narrative's picture

Great trick. Remainder of why, if it seems so straightforward and easy at first sight, it gotta be a trick question.

I think that if there are more than 2 colors of socks, A should be the answer to this question, since B becomes insufficient. We don't know how many colors of socks there are.
gmat-admin's picture

Hi ideree,

Many students have suggested this. However, it makes no difference whether there are socks a color different from white or black.

If you're not convinced, try to find a scenario in which a 3rd color makes statement 2 insufficient.


Wonderful Question :)

Does it help to know through statement 2 that the probability that the socks are not white is less than 0.4?
gmat-admin's picture

Statement 2 helps us reduce the possible number of black socks. It indirectly tells us that there are either 0 or 1 black socks.

If there are 0 black socks, then it's impossible to select 2 black socks without replacement.
So, the answer to the target question is, "The probability is 0 that we select 2 black sock with replacement"

If there is 1 black sock, then it's impossible to select 2 black socks without replacement.
So, the answer to the target question is, "The probability is 0 that we select 2 black sock with replacement"

So, statement 2 is sufficient.

You mean Statement 2 is sufficient?

gmat-admin's picture

Oops - good catch!!
I edited my response.


Hi Brent,

Could you please provide a solution to this question,

After reading a few comments I still don't understand it:

Thank you in advance,
gmat-admin's picture

Hi Brent,

Thank you very much,

Hi brent,

Can you elaborate how can we assume there are no more than 2 colors for socks ?

gmat-admin's picture

Hi Karaan,

We don't necessarily know there are only 2 colors.
From statement 1, we know that the drawer contains either 1 black sock or 0 black socks.
From statement 2, we know that the drawer contains either 5 white socks or 6 white socks.

When we combine the statements we see that there are exactly three possible outcomes:
1) 1 black sock, and 5 white socks
2) 0 black socks, and 6 white socks
3) 0 black socks, 5 white socks and 1 other sock

Having said that, all that really matters is that we don't have 2 black socks, which means P(selecting 2 black socks) = 0


hi Brent,

Could you please solve this question?

Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?

A. 66
B. 67
C. 68
D. 69
E. 70

gmat-admin's picture

I've included the answer choices since they're crucial to solving the question.

First notice that there's no way to get sums of 1¢ and 3¢
Now notice that we can't get sums of 69¢ and 67¢
How do we know this?
Since we have a total of 70¢, we'd need to remove a 1¢ coin to get a sum of 69¢. Since there are no 1¢ coins, we can't get 69¢.
Similarly, we'd need to remove a 3¢ coin to get a sum of 67¢. Since there are no 3¢ coins, we can't get 67¢.

There are 70 values from 1¢ to 70¢ inclusive.
We can't make 4 sums (1¢, 3¢, 67¢ and 69¢)
70 - 4 = 66
So there must be a total of 66 possible sums.
Answer: A

Thanks, Brent. Your solutions are really helpful in understanding the problems better. Can you please also solve this one?

A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.
(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

Thank you! :)
gmat-admin's picture

Karishma has a great solution (with diagrams) here:

Let me know if you have any questions about her solution.


Hey Brent,
Do you have a visual solution of this using venn diagrams?
gmat-admin's picture

Here's my full solution using the Double Matrix method:

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