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is a/b > c/d?

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by sanju09 » Fri Oct 07, 2011 4:36 am
If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.
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Source: — Data Sufficiency |
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by shankar.ashwin » Fri Oct 07, 2011 4:49 am
E IMO
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by sanju09 » Fri Oct 07, 2011 5:00 am
shankar.ashwin wrote:E IMO
Correct! What's your reasoning, by the way?
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by Anurag@Gurome » Fri Oct 07, 2011 5:08 am
sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.
(1) a > c
If a = 5, b = 10, c = 2, d = 8, then a/b = 5/10 = 1/2 and c /d = 2/8 = 1/4; here a/b > c/d
If a = 5, b = 20, c = 2, d = 4, then a/b = 5/20 = 1/4 and c /d = 2/4 = 1/2; here a/b < c/d
We do not get a definite answer; NOT sufficient.

(2) b > d
We can take the same examples as in statement 1; again statement 2 is NOT sufficient.

Combining (1) and (2) also, if we take the same examples as in statement 1, again we do not get a definite answer; NOT sufficient.

The correct answer is E.
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by shankar.ashwin » Fri Oct 07, 2011 5:12 am
Its definitely not A,B or D for we cannot compare numerators alone or denominators alone.

Together, we know a>c and b>d,

But we can have multiple possibilities for this,

2/10 > 1/8, you could also have 2/10<1/2.

Both satisfies the conditions. So E
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by GMATGuruNY » Fri Oct 07, 2011 8:34 am
sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.
Since the question is restricted to positive integers, it can be rephrased:

Is ad > bc?

Maximize a and d, minimize b and c, while satisfying the two statements:
a=10, d=10, b=11, c=1.
ad > bc.

Minimize a and d, maximize b and c, while satisfying the two statements:
a=10, d=1, b=100, c=9.
ad < bc.

Since the combinations above satisfy both statements, and in the first case ad > bc and in the second case ad < bc, INSUFFICIENT.

The correct answer is E.
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by parul9 » Fri Oct 07, 2011 8:01 pm
E! :)
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by abhi0697 » Sat Oct 08, 2011 6:38 pm
sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.


Kindly check out the below link for video solution:


https://www.youtube.com/watch?v=hEtUJyVs-KY

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by saketk » Mon Oct 10, 2011 3:55 am
Typically this type of questions can be solved by picking absolute values. Mitch has provided a wonderful explanation for this. IMO E
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by Whitney Garner » Mon Oct 10, 2011 7:37 pm
sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.
We can use simple theory as well. Because everything is positive, we can cross multiply (which is nice because it is easier to compare products than fractions).

a/b > c/d ?

ad > bc?

Statement (1): a>c
So one piece on the left side is bigger than one piece on the right side, but we don't know about the relative sizes of d and b so we have no clue.

Statement (2): b>d
So one piece on the right side is bigger than one piece on the left side, but we don't know about the relative sizes of a and c so we have no clue.

Statements Together: a>c and b>d
The problem is that we have split up the big pieces. One is on the left side (the a) and one is on the right side (the b). So each side has 1 bigger piece and 1 smaller piece, so there is NO way to tell which one rules the other.

Think about how this is different from an example like:
If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) d > b.
Now all the bigger stuff is on one side and all the smaller stuff is on the other. It is clear (together) that we have enough info!

:)
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by smackmartine » Mon Oct 10, 2011 8:07 pm
IMO E

(1) a > c. (we don't know anything about b,d) - Insufficient

(2) b > d. (we don't know anything about a,c) - Insufficient

Combining (1) and (2)

(a=1/2) > (c=1/3) and (b=2) >(d=1) -----------> 1/4 >1/3 (NO)

Also,
(a=3) > (c=2) and (b=1) >(d=1/2) -----------> 3 >1 (YES)

So, Insufficient.
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by sanju09 » Tue Oct 11, 2011 2:16 am
Whitney Garner wrote:
sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) b > d.
We can use simple theory as well. Because everything is positive, we can cross multiply (which is nice because it is easier to compare products than fractions).

a/b > c/d ?

ad > bc?

Statement (1): a>c
So one piece on the left side is bigger than one piece on the right side, but we don't know about the relative sizes of d and b so we have no clue.

Statement (2): b>d
So one piece on the right side is bigger than one piece on the left side, but we don't know about the relative sizes of a and c so we have no clue.

Statements Together: a>c and b>d
The problem is that we have split up the big pieces. One is on the left side (the a) and one is on the right side (the b). So each side has 1 bigger piece and 1 smaller piece, so there is NO way to tell which one rules the other.

Think about how this is different from an example like:
If a, b, c, and d are positive integers, is a/b > c/d?

(1) a > c.

(2) d > b.
Now all the bigger stuff is on one side and all the smaller stuff is on the other. It is clear (together) that we have enough info!

:)
Whit
Do you mean [spoiler]C[/spoiler] should be the answer, Whitney?

Oh! Now its alright on a second look.
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