All the T-shirts a clothing store stocks are plainand they are all in

Question

All the T-shirts a clothing store stocks are plain—and they are all in one of exactly four colors: blue, green, red, and yellow. On any day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts?

(1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined.

(2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

GMATCoachBen · Accepted Answer

Video solution here:

https://www.youtube.com/watch?v=hYX9hlgp4s4

stne · Answer

From the stem we know B = 2G

(1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined.

R+G>B
R+ B/2 >B
2R > B

INSUFF.

(2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined 
 
B> (R+Y )/2 
2B > R+Y

INSUFF.

1+2

2R >B
2B>R+Y

If R=4, B=5 and Y=2 , Yes to the stem.
If R=6, B=5 and Y=2 , NO to the stem.

INSUFF.

Ans E

Hope it helps.

deorapalak · Answer

How have we arrived at the number of sold items when we are checking both 1 and 2 statement together?

Posted from my mobile device

stne · Answer

If the numbers can satisfy the conditions given in the question then those numbers are valid.We can choose any number that satisfy the given statement(s).

Since If R=4, B=5 and Y=2 satisfy both (i) and (ii) these are valid numbers and we can answer YES to the stem.

Also since R=6, B=5 and Y=2 satisfy both (i) and (ii) these are also valid numbers and we can answer NO to the stem,

Since we cannot answer with certainly whether B >R both statements are still INSUFF.

Hope it helps.

Gemmie · Answer

B = 2G

?: B > R

Statement 1:
B < R + G
=> 2G < R + G
=> R < G
=> Insufficient

Statement 2:
B < 1/2 * (R + Y)
=> 2B < R + Y
=> 2B < G + Y
=> 2G < G + &
=> G < Y
=> Insufficient

Combined:
R < G < Y
And we only know B = 2G
=> Insufficient

daniazahid125 · Answer

From the stem we know B = 2G.(1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined: R+G>BR + G > BR+G>B R+G>2GR + G > 2GR+G>2G R>GR > GR>G

(2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined: B>R+Y2B > \frac{R + Y}{2}B>2R+Y​ 2B>R+Y2B > R + Y2B>R+Y 2(2G)>R+Y2(2G) > R + Y2(2G)>R+Y 4G>R+Y4G > R + Y4G>R+Y

Combining both statements: R>GR > GR>G 4G>R+Y4G > R + Y4G>R+Y

If R=4R = 4R=4, B=5B = 5B=5, and Y=2Y = 2Y=2, the condition holds: Yes to the stem. If R=6R = 6R=6, B=5B = 5B=5, and Y=2Y = 2Y=2, the condition does not hold: No to the stem.

Since we can find values where the conditions both satisfy and do not satisfy the stem, the information is insufficient.

Answer: E (Statements 1 and 2 together are still insufficient).

kanikaa9 · Answer

From statement 1 - #B can be > or < #R From statement 2 - #B can be > or < #R Even if we combine the two, we still have #B can be > or < #R . So E You can put values and check.

vanshitabajaj26 · Answer

can we not just take values and then proceed? b< r+ g and as b=2g so assuming g=1 so b will be atleast 2 and to satisfy the first statement we can take r=2,3etc. please help  Bunuel

Dream009 · Answer

I did with numbers - Let B= 20 and G = 10
ANd R = 12 or 40 - Statement 1 satisfies. Ans not sufficient

Statement 2 - don't know anything for red - answer no
together
let yellow be 25 R = 12 and and blue 20 - Blue is more than half
let yellow be 0 R = 42 and and blue 20 - Blue is more than half - Not suff -----ans E

All the T-shirts a clothing store stocks are plainand they are all in

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

All the T-shirts a clothing store stocks are plainand they are all in

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards