Magoosh
Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?
1) The total value of Mark's coins is $1.70.
2) Mark has three times as many quarters as he has dimes.
OA A
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Mark has fewer than 9 coins. Each coin is either a quarter
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Jay@ManhattanReview
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say Mark has x numbers of quarters and y numbers of dimes.AAPL wrote:Magoosh
Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?
1) The total value of Mark's coins is $1.70.
2) Mark has three times as many quarters as he has dimes.
OA A
Thus, we have
2 ≤ x + y < 9
We have to find out the value of y.
Let's take each statement one by one.
1) The total value of Mark's coins is $1.70.
0.25x + 0.10y = 1.70
5x + 2y = 43
y = (34 - 5x)/2
y = 17 - (5x)/2
Since x and y are integers, we must have x a multiple of 2.
To ensure that x + y < 9, only one value of x is valid, which is x = 6, thus, y = 2. Sufficient.
2) Mark has three times as many quarters as he has dimes.
x = 3y
To ensure that x + y < 9, we have y = 1 and x =3 or y = 2 and x = 6. No unique value of y. Insufficient.
The correct answer: A
Hope this helps!
-Jay
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GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
say Mark has x numbers of quarters and y numbers of dimes.AAPL wrote:Magoosh
Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?
1) The total value of Mark's coins is $1.70.
2) Mark has three times as many quarters as he has dimes.
OA A
Thus, we have
2 ≤ x + y < 9
We have to find out the value of y.
Let's take each statement one by one.
1) The total value of Mark's coins is $1.70.
0.25x + 0.10y = 1.70
5x + 2y = 43
y = (34 - 5x)/2
y = 17 - (5x)/2
Since x and y are integers, we must have x a multiple of 2.
To ensure that x + y < 9, only one value of x is valid, which is x = 6, thus, y = 2. Sufficient.
2) Mark has three times as many quarters as he has dimes.
x = 3y
To ensure that x + y < 9, we have y = 1 and x =3 or y = 2 and x = 6. No unique value of y. Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review
Locations: Manhattan Review Bangalore | GMAT Prep Chennai | GRE Prep Himayatnagar | Hyderabad GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
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GMATGuruNY
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Timer
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Your Answer
A
B
C
D
E
Global Stats
Statement 1:AAPL wrote:Magoosh
Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?
1) The total value of Mark's coins is $1.70.
2) Mark has three times as many quarters as he has dimes.
To MINIMIZE the number of coins so that a sum of 170 cents is yielded by at most 8 coins, we must MAXIMIZE the number of quarters.
Since 7*25 = 175 cents, the number of quarters must be less than 7.
170 cents will be yielded by 6 quarters (totaling 150 cents) and 2 dimes (totaling 20 cents), for a total of 8 coins and 170 cents.
Using fewer quarters will increase the number of coins beyond 8, violating the condition that Mark has fewer than 9 coins.
Implication:
No other combination of quarters and dimes is possible.
Thus, the number of dimes = 2.
SUFFICIENT.
Statement 2:
Case 1: 1 dime and 3 quarters, for a total of 4 coins
Case 2: 2 dimes and 6 quarters, for a total of 8 coins
Since the number of dimes can be different values, INSUFFICIENT.
The correct answer is A.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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