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

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

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28 Nov 2017, 23:33
00:00

Difficulty:

75% (hard)

Question Stats:

61% (01:56) correct 39% (01:46) wrong based on 115 sessions

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

(1) x – w = 5
(2) w > 25

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Concentration: Marketing, Social Entrepreneurship
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If x is greater than 105 percent of w, is x > 25?  [#permalink]

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29 Nov 2017, 00:56
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25

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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29 Nov 2017, 10:09
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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29 Nov 2017, 10:17
1
septwibowo wrote:
Bunuel wrote:
If x is greater than 105 percent of w, is x > 25?

(1) x – w = 5
(2) w > 25

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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29 Nov 2017, 12:58
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 $$100>25$$.

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

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29 Nov 2017, 22:29
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

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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30 Nov 2017, 06:32
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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04 Dec 2017, 10:45
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.

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Re: If x is greater than 105 percent of w, is x > 25?   [#permalink] 04 Dec 2017, 10:45
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