If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) b > d.
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is a/b > c/d?
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sanju09
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shankar.ashwin
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sanju09
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Correct! What's your reasoning, by the way?shankar.ashwin wrote:E IMO
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(1) a > csanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) b > d.
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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shankar.ashwin
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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
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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Since the question is restricted to positive integers, it can be rephrased:sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) b > d.
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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abhi0697
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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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Whitney Garner
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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).sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) b > d.
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:
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!If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) d > b.
Whit
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Math is a lot like love - a simple idea that can easily get complicated
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smackmartine
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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.
(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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sanju09
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Do you mean [spoiler]C[/spoiler] should be the answer, Whitney?Whitney Garner wrote: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).sanju09 wrote:If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) b > d.
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: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!If a, b, c, and d are positive integers, is a/b > c/d?
(1) a > c.
(2) d > b.
Whit
Oh! Now its alright on a second look.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
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Sanjeev K Saxena
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www.manyagroup.com
