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# If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)  [#permalink]

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24 Apr 2018, 04:47
00:00

Difficulty:

65% (hard)

Question Stats:

41% (01:53) correct 59% (01:39) wrong based on 82 sessions

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If r is greater than 120 percent of s, is r > 70?

(1) 60 < s < 80
(2) r - s = 40

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Senior Manager
Joined: 21 Jan 2015
Posts: 408
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
Re: If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)  [#permalink]

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24 Apr 2018, 05:02
And: D
Both statement alone sufficient to ans the question..

given r > 120% of s

from 1: minimum value of s is 60 so r must be greater than 120 % of 60 which is = 72 (Sufficient)
from 2: given r-s= 40 means 1.20s-s=40 so .2s=40: so s=200 thus r>70 (sufficient)

Both alone sufficient to ans.
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Joined: 18 Jul 2016
Posts: 34
Re: If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)  [#permalink]

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24 Apr 2018, 11:30
Given that
$$r > \frac{120}{100} s$$ ; $$r > 70 ?$$

Statement 1

$$60 < s < 80$$

For min value of s = 60, $$\frac{120}{100}* 60$$ => r > 72

Sufficient

Statement 2

$$r - s = 40$$

=> $$s = r- 40$$

=> $$r > \frac{120}{100}* (r-40)$$

=> $$r > \frac{6}{5} r - 48$$

=> $$r < 48 * 5$$

But we don't know if r > 70, hence Insufficient

IMO A
Manager
Joined: 05 Dec 2017
Posts: 52
Location: India
WE: Analyst (Commercial Banking)
Re: If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)  [#permalink]

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24 Apr 2018, 11:37
1
St1 : 60 < s < 80

Since r>1.2s, considering the lowest value of s,
r>1.2*60 or r >72
is r>70 with 60 < s < 80 => Yes
Sufficient

St2 : r - s = 40

Now r>1.2s
or r-s>0.2s
or 40>.2s
or s<200

Since there is no lower limit, and s can be zero also, r can take values on both side of 70

Hence insufficient

Correct Option A
Director
Joined: 02 Oct 2017
Posts: 735
Re: If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2)  [#permalink]

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11 May 2018, 22:29
Given r>6s/5

I) for s=60
r>6*60/5
r>72
So for other values r is surely greater than 70
Sufficient

II) r-s=40

R can be 30 s can be -10
Or
R can be 80 and s be 40
Many possibilities
So insufficient

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Re: If r is greater than 120 percent of s, is r > 70? (1) 60 < s < 80 (2) &nbs [#permalink] 11 May 2018, 22:29
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