If x is less than 75 percent of y, is x less than 75 ?

Question

(1) y > 20
(2) x + 25 = y

ydmuley · Accepted Answer

If x is less than 75 percent of y, is x less than 75?

\(x < 75%* y\)

\(x < \frac{75}{100} * y\)

Question, Is \(x < 75\) ?

In order to answer the above question, we need to find the value of y, as per the given expression:

\(x < \frac{75}{100} * y\)

x is < 75 when the value of y = 100

(1) \(y > 20\)

y > 20, in this case, y can take values which can be below 100 and greater than 100 as well. Hence, Eq. 1 is not sufficient.

Hence, (1) ===== is NOT SUFFICIENT

(2) \(x + 25 = y\)

After substituting this value in the below equation, we get, \(x = 75\)

This is sufficient to answer the question is x < 75, the answer is NO.

Hence, (2) ===== is SUFFICIENT

Hence, Answer is B

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Bunuel · Answer

Similar question from OG: https://gmatclub.com/forum/if-y-is-grea ... 66185.html

Luckisnoexcuse · Answer

x<0.75y is x<75

(1) y>20
if y = 40 then x <30 but if y=400 then x<300
not sufficient

(2)
x+25 = y
x= y-25
if y = 40 then x<30 and we get x = 15 (less than 75)
if y = 88 then x<66 and we get x=63 (less than 75)
if y=92 then x<69 and we get x = 67 (less than 75)
if y=96 then x<72 and we get x = 71
if y=94 then x<70.5 and we get x = 69
if y = 100 then x<75 and we get x = 75 not possible
For equation (x<0.75y) to hold y will be less than 100 and hence x will always be less than 75
Sufficient

B
Any shortcut

Its_me_aka_ak · Answer

i dont understand.
if Y is 125 and X is 100 as per statement 2 then X is more than 75% of y. how is it sufficient

Its_me_aka_ak · Answer

why cant Y be more than 100?

guipjf · Answer

Assertion from the question stem:
x < 0.75*(y)

Question:
x<75?

Statement 1:
y>20

y could be 20 or 200. 
If y=200, then, according to the assertion, we would have x<150, which does not answer our question since x could be 100 or 1.
If y=20, then, x<15, which answer the question since any number less than 15 is less than 75 as well.

Hence, (1) is insufficient.

Statement 2:
y = x+25

If we substitute this statement in the assertion of the text, we would have: x<0.75*(x+25). Simplifying this, we would have: x<75.

Hence, (2) is sufficient.

Its_me_aka_ak · Answer

difference gotta be 25, go it last time i was a bit out of focus thanks

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If x is less than 75 percent of y, is x less than 75 ?

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If x is less than 75 percent of y, is x less than 75 ?

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