Princeton Review
A drawer contains 12 socks, of which 8 are black and 4 are white. If 3 of the socks are removed, how many of the socks that remain in the drawer are black?
(1) The socks that remain in the drawer have a ratio of 2 black to 1 white.
(2) One of the first two socks removed is black.
OA A.
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
A drawer contains 12 socks, of which 8 are black and 4 are
This topic has expert replies
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
Let's take each statement one by one.AAPL wrote:Princeton Review
A drawer contains 12 socks, of which 8 are black and 4 are white. If 3 of the socks are removed, how many of the socks that remain in the drawer are black?
(1) The socks that remain in the drawer have a ratio of 2 black to 1 white.
(2) One of the first two socks removed is black.
OA A.
(1) The socks that remain in the drawer have a ratio of 2 black to 1 white.
Say the out of the 3 removed socks, x were black, thus, (3 - x) were white.
Number of black socks (now) = 8 - x;
Number of white socks (now) = 4 - (3- x) = 1 + x;
Ratio of Black socks to White socks = (8 - x) : (1 + x) :: 2 : 1
=> x = 2
The number of socks that remain in the drawer black = 8 - 2 = 6. Sufficient.
(2) One of the first two socks removed is black.
We have no information about the third. Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan Review Mehdipatnam | Hyderabad GMAT Prep | Bangalore GMAT Courses | Dilsukhnagar GRE Prep | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
After removing three socks
remaining socks =12-3 = 9 socks
The 3 socks removed could be either 3 blacks, 3 whites , 1 black and 2 whites, 2 blacks and 1 white
$$let\ black\ =B\ and\ white\ =W$$
Statement 1
The socks that remain in the drawer have a ratio of 2B to 1W
$$9\ socks\ =\frac{\left(2B+2B+2B\right)}{\left(1W+1W+1W\right)}=\frac{6B}{3W}=6B:2W$$
Hence, there are 6 Blacks remaining in the drawer.
$$Statement\ 1\ is\ INSUFFICIENT$$
Statement 2
One of the first two socks removed is black, This means that from the first two socks removed, at least one of them is Black.
From the question, three socks were removed from the three socks there are two different possibilities;
1B and 2W or 2B and 1W ; this information doesn't tell us about the remaining 9 socks.
Hence Statement 2 is INSUFFICIENT
Statement 1 alone is SUFFICIENT
$$answer\ is\ option\ A$$
remaining socks =12-3 = 9 socks
The 3 socks removed could be either 3 blacks, 3 whites , 1 black and 2 whites, 2 blacks and 1 white
$$let\ black\ =B\ and\ white\ =W$$
Statement 1
The socks that remain in the drawer have a ratio of 2B to 1W
$$9\ socks\ =\frac{\left(2B+2B+2B\right)}{\left(1W+1W+1W\right)}=\frac{6B}{3W}=6B:2W$$
Hence, there are 6 Blacks remaining in the drawer.
$$Statement\ 1\ is\ INSUFFICIENT$$
Statement 2
One of the first two socks removed is black, This means that from the first two socks removed, at least one of them is Black.
From the question, three socks were removed from the three socks there are two different possibilities;
1B and 2W or 2B and 1W ; this information doesn't tell us about the remaining 9 socks.
Hence Statement 2 is INSUFFICIENT
Statement 1 alone is SUFFICIENT
$$answer\ is\ option\ A$$
