Hallie has only nickels, dimes and quarters in her pocket. If she has

Question

Hallie has only nickels, dimes and quarters in her pocket. If she has at least 1 of each kind of coin and has a total of $2.75 in change, how many nickels does she have?

(1) She has a total of 21 coins, with twice as many dimes as nickels.
(2) She has $1.50 in quarters.

Kudos for a correct  solution .

askhere · Answer

Let N n , N d , and N q  be the number of nickels dimes and quarters.
From the question stem we know that:
0.05N n  + 0.10N d  + 0.25N q  = 2.75

Statement 1: N n  + N d  + N q  = 21 & N d  = 2N n 
i.e 
N n  + 2N n  + N q  = 21
3N n  + N q  = 21 -------------------------------------- (1)

0.05N n  + 0.10* 2N n  + 0.25N q  = 2.75
0.25N n  + 0.25N q  = 2.75
N n  + N q  = 11 ---------------------------------------- (2)
So from (1) & (2) one can calculate number of nickels.  A is sufficient

Statement 2:
0.25N q  = 1.5
N q  = 6
Since we don't have any information about total number of coins we have only one equation with two unknowns
i.e. 0.05 N n  + 0.1N d  = 1.25. So insufficient.

Answer :  A

Ambarish

EMPOWERgmatRichC · Answer

Hi All,

As "thick" as this prompt might look, it has a great "System Math" shortcut built into it that will help you to answer this question without having to do that many calculations:

We're told that there are only nickels (0.05 each), dimes (0.10 each) and quarters (0.25 each) in Hallie's pocket, that she has AT LEAST 1 of each kind of coin and that the total is $2.75. We're asked how many nickels she has.

For organizational purposes, I'm going to use the following variables:
N = number of nickels
D = number of dimes
Q = number of quarters

From the prompt, we can create one equation:

.05N + .1D + .25Q = 2.75

This is 1 equation with 3 variables. To figure out the number of nickels, we need EITHER the number of dimes AND the number of quarters OR we need 2 more unique equations.....

Fact 1: She has a total of 21 coins, with twice as many dimes as nickels.

While it might be tempting to create one "big" equation from this information, we can create two separate equations:

N + D + Q = 21
D = 2N

Combined, with the original equation from the prompt, we now have a "System" of equations (3 variables and 3 unique equations), so we CAN solve for each variable and answer the question (without having to do all of that math).
Fact 1 is SUFFICIENT

Fact 2: She has $1.50 in quarters.

We can substitute this information into the original equation:

.05N + .1D + 1.50 = 2.75
.05N + .1D = 1.25

Unfortunately, there are many different ways to get 1.25 using nickels and times.

eg.
N = 1, D = 12
N = 3, D = 11
N = 5, D = 10
Etc.
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

akhilbajaj · Answer

The equation may be written as 0.05N+0.1D+0.25Q=2.75
St1
N+D+Q=21
D-2N
We have 3 equations for 3 variables which can be solved. Sufficient

St2
0.05N+0.1D=1.25
This may be simplified to
5N+10D=125, or
N+2D=25
This equation may have many solutions. Insufficient.

Answer A

Bunuel · Answer

KAPLAN OFFICIAL SOLUTION:

Now this question is certainly answerable. You might have to play with the information, do a little substitution, a little combination, but eventually you’d figure out that she had 5 nickels. Now what do you do with that number? There is no answer choice for 5. There is no way to enter your discovery at all. Strictly speaking the information is useless.

Furthermore, if you focused on answering the question about Hallie’s nickels instead of the data sufficiency question that is being asked, chances are that you would use all the information given in both statements instead of considering them separately. (The problem is easier to solve if you do.) In that case, you will perhaps conclude that the statements taken together are sufficient to answer the question, when in fact, statement 1 by itself is sufficient.

Lastly, this whole process of solving for the number of nickels takes a lot of time-- time you probably wish you could use on other problems.

So how would a “lazy person” approach this question? The lazy person would never just dive in and start sifting information, but would take a bird’s-eye view. He or she would look for the concept. Data Sufficiency is concept math.

Our lazy student would look at the question stem and see that there are three unknowns (nickels, dimes and quarters), that they total up to a definite amount and that he is being asked for the value of one of them separately. That would strongly suggest a system of equations.

Next our lazy student would recall the rule for systems of equations, which is that you must have as many distinct equations as you have variables in order to solve for the individual variables. How many equations does the stem give us? One, for the total dollars. So we need two more.

Statement 1 gives us two more. That there are 21 coins would give us one equation, and that there are twice as many dimes as nickels would give us the other. (Note, an equation to be useful does not have to have all the variables in it, so the lack of quarters in the second equation doesn’t matter.) Together with the stem, that makes three equations, which allow us to solve the system (which we needn’t bother to do).

Statement 2 only gives us one more equation, so it is not sufficient, and the answer is Statement 1 alone is sufficient.
Notice that our lazy student did not even bother to translate the words into formal equations. It’s enough to know that you COULD do so.

So if you find yourself tempted to do extensive mathematical calculations on a GMAT Data Sufficiency problem—remember the “lazy student”, and that the secret on Data Sufficiency problems is that the answer to the mathematical question doesn’t matter in most instances. Keep your eye on the concept being tested rather than the details of the execution.

~By Guest Author, Kurt Keefner

Hahshsh · Answer

I can't figure out how the answer is option a. Can someone post a detailed explanation?

Bunuel · Answer

Detailed explanations are posted above. Please read the thread.

bumpbot · Answer

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Hallie has only nickels, dimes and quarters in her pocket. If she has

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