Rick can solve x algebra problems per minute. Matt can solve y calculu

Question

Rick can solve x algebra problems per minute. Matt can solve y calculus problems per minute. If y is not equal to zero, is x/y > 3?

(1) x > 3
(2) –(x/y) < 3

bankerboy30 · Accepted Answer

Doesn't it become x/y>-3?

EMPOWERgmatRichC · Answer

Hi All,

Certain DS questions on the Official GMAT will include a "redundant" piece of information in one (or both) of the two Facts. By 'redundant', I mean that it is information that was either already given in the prompt (or something that you can deduce from the information in the prompt). Redundant Facts are always insufficient (since you already had the information, the Fact does not offer anything new).

Here, we're told that Rick can solve X problems per minute and Matt can solve Y problems per minute. Neither of these 2 variables can be negative (a person cannot solve "negative" problems in the context of this question). We're also told that Y CANNOT be 0. As such, X/Y is either 0 or it's positive, so the information that -(X/Y) < 3 is redundant, since -(X/Y) is either 0 or it's negative and ALL of those possibilities are LESS than +3. Thus, Fact 2 is INSUFFICIENT.

While redundant information isn't that common on the Official GMAT, you'll likely have to deal with it at least once, so it's important to take the proper notes and make whatever deductions you can with the information that appears in the prompt.

GMAT assassins aren't born, they're made,
Rich

sterling19 · Answer

Statement 1:  x > 3 does not give any information on y and x could be an infinite number of values 
Statement 2:  dividing by a negative value in an inequality reverses the sign so if we divide both sides of the inequality by -1 then -(x/y) < 3 becomes (x/y) > 3 which is sufficient to answer the question.

The correct answer is B.

Temurkhon · Answer

R=x/min, so x>=0 and integer
M=y/min, so y>0 and integer
Question: Is x/y>3 or x more than three times more than y? Yes/No question

St.1. x>0. No information about y. INSUFF

St.2. -(x/y)<3 => x/y>-3 means that x/y can be 0,1,2,3 or >3. INSUFF

St.1+St.2. Just exclude x/y=0 but still makes 1,2,3 or >3 possible. INSUFF

E

DesiGmat · Answer

Here we go:

y is not equal to zero (given)

St1: x > 3

No information is given for Y.

Clearly Insufficient.

St2: –(x/y) < 3

x/y > -3

x = 1, y = 1 (x/y > -3, but x/y is not > 3)

x = 8, y = 2 (x/y > -3, and x/y > 3)

Two solutions possible..
Clearly Insufficient.

Combining

We are talking in terms of efficiency of X and Y.

Take x = 4 and Y = 3 (x/y is not > 3)
Take x = 4 and Y = 1 (x/y > 3)

Two possible solutions.

Clearly E is the answer.

chetan2u · Answer

hi empower ,
 u are right that many times, there are redundant information...
But not in this case. Its very importantto read finer point between the lines..
it gives the speed as problems per minute.. now either a problem is solved or not solved, we cannot have a half solved problem..
this does mean that x and y are integers....
this is what i feel, although it may be possible the Q was not meant that way..

EMPOWERgmatRichC · Answer

Hi chetan2u,

If you reread my post, you'll see that I made no reference to whether X and Y were integers or not (that point is irrelevant), only that X/Y had to be 0 or positive. As such -(X/Y) will EITHER be 0 or a negative value, so -(X/Y) will ALWAYS be less than 3, regardless of the values.

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

hi rich...
 you may not have meant it, so it's perfectly fine. but my point is in general that even a sentence such as 'Rick can solve x algebra problems per minute. Matt can solve y calculus problems per minute'. can give us a point to move on... but as you say it was statement two which is renundant. this too may not be correct as the Q says x/y>3 and statement 2 when simplified tells us x/y>-3.. two different things..
i think i actually require to read Q again .. but kudos to you...

sterling19 · Answer

Yes, you're right.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION: Solution: E Statement (1) only tells us about x; INSUFFICIENT. Statement (2) can be rewritten as (-x)/y < 3. Y cannot be negative – no one does “negative” calculus problems per minute – so it must be positive. This means that we can multiply both sides by y knowing that the sign won’t flip, so –x < 3y. Multiplying both sides by -1 gives us x > -3y, and dividing by y gives us x/y > -3; INSUFFICIENT. Combined the statements are still insufficient: we could have x/y = 5/1, as that’s greater than -3, and we could have x/y = 4/3, as that’s also greater than -3. (E).

mvictor · Answer

xexe...this one wants to trick you to pick B...
1 clearly insufficient.
2 multiply both sides by -1, and flip the inequality sign: x/y > -3 - not sufficient

1+2
x=4, y=2, nope
x=4, y=1, yes

1+2 not sufficient.

answer is E.

nn2015 · Answer

Answer: E
S#1: x > 3
Mentioned about only x, so not sufficient

S#2: 
–(x/y) < 3
x/y > -3

'> -3' only gives the starting range of the possible values that x/y can have, so we can come up with different values of x/y
case 1: x/y = 5, which satisfies x/y > -3, giving us YES for x/y >3
case 2: x/y = 2, which satisfies x/y > -3, giving us NO for x/y > 3
Therefore, not sufficient

S#1 + S#2:
x > 3 and x/y > -3 
These give only the starting range of the possible values x/y can have, so we can come up with different values of x/y

case 1: x/y = 15/3 = 5, which satisfies x>3 and x/y > -3, giving us YES for x/y >3
case 2: x/y = 4/2 = 2, which satisfies x>3 and x/y > -3, giving us NO for x/y > 3

Therefore, not sufficient. Answer E.

RMD007 · Answer

IMO: E

Statement 1 : clearly insufficient.
Statement 2 : Since we know that x and y are rates. They can not be negative.
(x/y)>0
Hence -(x/y)<0.
So -(x/y)<3 is not useful.

saurabhsavant · Answer

well...i guess we both made the same silly mistake-forgot to change the sign of "3"...arghhh.

CEdward · Answer

Suppose we didn't know anything about rates. This could be solved using number properties.

St1. x> 3
Insufficient since we don't know y.

St2. x/y > -3
x = 3, y = 1 NO
x = 4, y = 1 YES
Insufficient

Combined:
x = 4, y = 1 YES
x = 4, y = 2 NO

E

Bambi2021 · Answer

I made the same mistake.

Note to self: If you flip the signs on both sides of an inequality, you can also flip the mouth of the crocodile. You can't just delete the negative sign and flip the mouth!

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Rick can solve x algebra problems per minute. Matt can solve y calculu

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