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Posts: 1,925
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
46% (02:24) correct
54%
(02:25)
wrong
based on 108
sessions
History
Date
Time
Result
Not Attempted Yet
Are negative integers \(s\) and \(t\) both less than \(r\) ?
1) \(s < r+t\)
2)\(\frac{s}{r}\)\(<t\)
1) \(s < r+t\)
2)\(\frac{s}{r}\)\(<t\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
gmatbusters
Statement 1: \(s < r+t=>r>s-t\)
if \(s=-1\) and \(t=-4\) then \(r>-1+4=>r>3\). hence we have a Yes for our question stem
but if \(s=-5\) and \(t=-2\), then \(r>-5+2=>r>-3\), so \(r\) could be \(-2\). in this case \(r=t\) so we have a NO. Insufficient
Statement 2: \(\frac{s}{r}\)\(<t\)
\(=>\frac{s}{rt}>1\), now \(s\) & \(t\) are negative. hence \(\frac{s}{t}\) is positive. so we have
\(\frac{positive}{r}>1 => r>0\). Hence we have a Yes for our question stem. Sufficient
Option B
Posts: 3,651
![Are negative integers s and t both less than t? 1) s < r+t 2)[m][fract](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Are negative integers s and t both less than t? 1) s < r+t 2)[m][fract"){kind=icon}
Updated on: 22 May 2018, 10:30
Originally posted by EgmatQuantExpert on 22 May 2018, 02:26.
Last edited by EgmatQuantExpert on 22 May 2018, 10:30, edited 1 time in total.
Last edited by EgmatQuantExpert on 22 May 2018, 10:30, edited 1 time in total.
Solution
Given:
• Both s and t are negative integers
To find:
• Whether the value of s and t less than r
Analysing Statement 1
• As per the information given in Statement 1, s < r + t
- o Or, r > s – t
Depending on the values of s and t, r can belong to any of the regions indicated.
For example, if s = -7 and t = -1, r > (-7) – (-1) or r > -6
Now, r > -6 means r belong to any of the 3 regions indicated above (red, blue, green)
Hence, statement 1 is not sufficient to answer
Analysing Statement 2
• As per the information given in Statement 2, \(\frac{s}{r}\) < t
• We know that t is negative. Hence \(\frac{s}{r}\) should also be negative.
• We know that s is already negative. Thus, to ensure that \(\frac{s}{r}\) is negative. r MUST be positive.
Hence, from the given statement \(\frac{s}{r}\) < t, we can say r > 0 and \(\frac{s}{t}\) > 0
Hence, statement 2 is sufficient to answer
Hence, the correct answer is option B.
Answer: B
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gmatbusters
Similar question to practice: https://gmatclub.com/forum/are-negative ... 25947.html
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EgmatQuantExpert
Hi EgmatQuantExpert
May be I am missing something here. kindly explain the highlighted part. how are we arriving at \(r>\frac{s}{t}\). we know \(t\) is negative and we know nothing about \(r\). so if you are cross-multiplying \(t\) then sign of inequality should change.
Eventually \(r\) will be positive.
Posts: 1,925
Hi
The best approach to consider statement 2 is as follows:
2) s/r <t
as we know that s and t are negative,
So if r is also negative, then s/r would be positive and this inequality s/r <t would not be valid .
So r is positive. hence s and t are both less than r .
SUFFICIENT.
The best approach to consider statement 2 is as follows:
2) s/r <t
as we know that s and t are negative,
So if r is also negative, then s/r would be positive and this inequality s/r <t would not be valid .
So r is positive. hence s and t are both less than r .
SUFFICIENT.
niks18
Posts: 1,925
Hi niks18
Your Query: May be I am missing something here. kindly explain the highlighted part. how are we arriving at \(r>\frac{s}{t}\). we know \(t\) is negative and we know nothing about \(r\). so if you are cross-multiplying \(t\) then
sign of inequality should change.- Since we don't know the nature of r, we can not predict the nature of sign of inequality at this stage of time, without determining the nature of sign of r..
Hi EgmatQuantExpert
May be I am missing something here. kindly explain the highlighted part. how are we arriving at \(r>\frac{s}{t}\). we know \(t\) is negative and we know nothing about \(r\). so if you are cross-multiplying \(t\) then sign of inequality should change.
Eventually \(r\) will be positive.[/quote]
Your Query: May be I am missing something here. kindly explain the highlighted part. how are we arriving at \(r>\frac{s}{t}\). we know \(t\) is negative and we know nothing about \(r\). so if you are cross-multiplying \(t\) then
sign of inequality should change.- Since we don't know the nature of r, we can not predict the nature of sign of inequality at this stage of time, without determining the nature of sign of r..
niks18
Hi EgmatQuantExpert
May be I am missing something here. kindly explain the highlighted part. how are we arriving at \(r>\frac{s}{t}\). we know \(t\) is negative and we know nothing about \(r\). so if you are cross-multiplying \(t\) then sign of inequality should change.
Eventually \(r\) will be positive.[/quote]
Posts: 3,651
niks18
Hi niks,
You are correct! We cannot infer anything about the range of r. Ideally we can only say that:
- • As both s and t are negative integers, the right-hand side of the given expression is negative. But \(\frac{s}{t}\) is positive.
• Given that s is also negative, it means r is positive
Have edited the solution. Apologies for the confusion.
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1) s<r+t
Remember we don't know sign of r
So multiple cases arise
1) -6<-2-3
s=-6 r=-2 t=-3. S and t are less than r
2)-6<-3-2
s=-6 r=-3 t=-2. S is less than r but t is not
So Insufficient
2)s/r<t
S and t are given as negative integers
R cannot be negative here as it would result in positive value on left side
Whereas on the left side we have negative value
So r is positive and t and s are less than r as they are negative
Sufficient
B is answer
Give kudos if it helps
Posted from my mobile device
Remember we don't know sign of r
So multiple cases arise
1) -6<-2-3
s=-6 r=-2 t=-3. S and t are less than r
2)-6<-3-2
s=-6 r=-3 t=-2. S is less than r but t is not
So Insufficient
2)s/r<t
S and t are given as negative integers
R cannot be negative here as it would result in positive value on left side
Whereas on the left side we have negative value
So r is positive and t and s are less than r as they are negative
Sufficient
B is answer
Give kudos if it helps
Posted from my mobile device
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