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27 Aug 2006, 03:47
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If x and y are positive is 3x>7y?
1) x>y+4
2) -5x<-14y
1) x>y+4
2) -5x<-14y
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Hi there,
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27 Aug 2006, 04:22
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apollo168
Since we know that both x and y are positive, we can try substituting numbers for x and y in statement 1.
According to x > y+4, if y is 0.1, then x > 4.1
Putting 4.1 and 0.1 in place of x and y in the stem inequality i.e 3x>7y, we get
3(4.1) > 7(0.1) ----- True
Now, try putting 3 for y in statement 1, we get x > 7.
Substitute x by 7 and y by 3 in our question, we get
3(7) >7(3) -------- False
Therefore, statement 1 is insufficient.
Statement 2 can also be written as,
5x > 14y
or, x > (14/5)y
Now, substituting y with 0.1, we get
x > (14/5)*0.1 (approx, 0.28)
x > 0.28
Putting this value in 3x>7y, we get the following values:
x = 0.84
y = 0.7 ------ True
try, substituting y with 5, we get
x> (14/5)*5
x>14
Putting this value in 3x>7y, we get the following values:
x=52
y=35 ---------- True
try, substituting y with 10, we get
x> (14/5)*10
x>28
Putting this value in 3x>7y, we get the following values:
x=84
y=70---------- True
therefore, i conclude that statement 2 is sufficient.
Hence, my answer is B.
Sorry if this was a little hard to understand.
SHA.
27 Aug 2006, 04:27
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apollo168
Hi no its ok I also arrived at B, by manipulating the question stem to read
(x/y)>7/3?
I thought statement 1 was clearly insufficient. So I proceeded to statement 2 manipulating the inequality I arrived at x/y >14/5 which is clearly sufficient. However the OA at least according to the answer key is D. Which still has me perplexed
