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If x is greater than 105 percent of w, is x > 25?

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If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 00:33
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  65% (hard)

Question Stats:

58% (01:25) correct 42% (01:09) wrong based on 113 sessions

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If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 01:56
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25


Try to answer :

Question :
- \(X>\frac{(105w)}{100}\); \(x>25\)?

Statement 1
- \(x-w=5\) -> \(x=w+5\).
- Plug into initial inequality : \(w+5>\frac{(105w)}{100}\) -> \((100)w+5>(105w)\) -> \(100w+500>105w\) -> \(5w<100\) or \(w<20\)
- Then, if \(w=20\), X must be less than 25.
- SUFFICIENT.

Statement 2 itself sufficient.

D.
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Re: If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 11:09
1
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25


x > 1.05w... x-w>.05w
From Stmn1: 5>w/20.. w < 100..Not Sufficient.
From Stmn2: x > 1.05 w.. sufficient
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Re: If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 11:17
1
septwibowo wrote:
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25


Try to answer :

Question :
- \(X>\frac{(105w)}{100}\); \(x>25\)?

Statement 1
- \(x-w=5\) -> \(x=w+5\).
- Plug into initial inequality : \(w+5>\frac{(105w)}{100}\) -> \((100)w+5>(105w)\) -> \(100w+500>105w\) -> \(5w<100\) or \(w<20\)
- Then, if \(w=20\), X must be less than 25.
- SUFFICIENT.

Statement 2 itself sufficient.

D.


Hi septwibowo

the highlighted portion is incorrect, hence you got option A as sufficient. it should be w<100.
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If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 13:58
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25




\(x>\frac{21w}{20}\) ; \(20x>21w\). \(x>25?\)

\(w>25....(II)\)... Sufficient

\(x-w= 5...(I)\)... Insufficient, i.e \(5.5- 0.5= 5\) fufills the constraint , yet \(5.5<25\) and \(100-95= 5\) also does, but \(100>25\).

Hence, the answer is B.
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Re: If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 29 Nov 2017, 23:29
niks18 wrote:
septwibowo wrote:
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25


Try to answer :

Question :
- \(X>\frac{(105w)}{100}\); \(x>25\)?

Statement 1
- \(x-w=5\) -> \(x=w+5\).
- Plug into initial inequality : \(w+5>\frac{(105w)}{100}\) -> \((100)w+5>(105w)\) -> \(100w+500>105w\) -> \(5w<100\) or \(w<20\)
- Then, if \(w=20\), X must be less than 25.
- SUFFICIENT.

Statement 2 itself sufficient.

D.


Hi septwibowo

the highlighted portion is incorrect, hence you got option A as sufficient. it should be w<100.


Ahhhh! my bad! Thanks anyway niks18 !
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Re: If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 30 Nov 2017, 07:32
Simplifying the question stem

It becomes x > 1.05 W, then the question is asking whether x > 25?

1) x - w =5

This will be x = 5 + w which may yield a yes or no. so insufficient if w = 5 then x = 10 <25 no. However, if w = 30 then x = 35 > 25 yes.
Getting two answers makes the statement insufficient.

2) w > 25, given that x > 1.05w then x > 25 yes.

B is sufficient.
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Re: If x is greater than 105 percent of w, is x > 25? [#permalink]

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New post 04 Dec 2017, 11:45
2
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25


We have that x > 1.05w, and need to determine whether x > 25.

Statement One Alone:

x - w = 5

Thus, x - 5 = w, so we have:

x > 1.05(x - 5)

x > 1.05x - 5.25

5.25 > 0.05x

525 > 5x

105 > x

We see that x is less than 105, but it doesn’t mean x is greater than 25. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

w > 25

Since x >1.05w and w > 25, x must also be greater than 25.

Answer: B
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Re: If x is greater than 105 percent of w, is x > 25?   [#permalink] 04 Dec 2017, 11:45
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