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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Mark has fewer than 9 coins. Each coin is either a quarter tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Mark has fewer than 9 coins. Each coin is either a quarter ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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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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 say Mark has x numbers of quarters and y numbers of dimes. 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.

Hope this helps!

-Jay
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### GMAT/MBA Expert

GMAT Instructor
Joined
22 Aug 2016
Posted:
1766 messages
Followed by:
28 members
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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 say Mark has x numbers of quarters and y numbers of dimes. 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.

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Bangalore | GMAT Prep Chennai | GRE Prep Himayatnagar | Hyderabad GRE Coaching | and many more...

### GMAT/MBA Expert

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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. Statement 1: 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. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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