Mark has fewer than 9 coins. Each coin is either a quarter

This topic has expert replies
Moderator
Posts: 2205
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: Magoosh

Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime ($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.

The OA is A.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 20, 2018 5:38 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorLU wrote:Source: Magoosh

Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime ($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:
25Q + 10D = 170
5Q + 2D = 34
To minimize the number of coins, we must maximize the value of Q.
If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34.
In this case, the total number of coins = 6+2 = 8.
If the value of Q decreases, then the total number of coins will have to increase and thus not be less than 9.
Implication:
For the total number of coins to be less than 9, Q=6 and D=2.
SUFFICIENT.

Statement 2:
Case 1: D=1 and Q=3, for a total of 4 coins
Case 2: D=2 and Q=6, for a total of 8 coins
Since D can be different values, INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
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.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3