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B
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Difficulty:
55%
(hard)
Question Stats:
62% (01:53) correct
38%
(02:12)
wrong
based on 226
sessions
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12 Days of Christmas GMAT Competition with Lots of Fun
Is m+10 positive?
(1) On the number line, m+10 is closer to 0 than to m.
(2) On the number line, m -10 is closer to 0 than to m.
Is m+10 positive?
(1) On the number line, m+10 is closer to 0 than to m.
(2) On the number line, m -10 is closer to 0 than to m.
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General Discussion
23 Dec 2021, 10:09
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Question Stem:
Is m+10 positive?
(1) On the number line, m+10 is closer to 0 than to m.
(2) On the number line, m -10 is closer to 0 than to m.
Solution:
Statement 1:On the number line, m+10 is closer to 0 than to m.
Now since this talks about the relative distance from 0, we can use modulus.
If I were to state Statment in mathematical terms, I would write |m|>|m+10|.
Now, critical points for this equation are -10 and 0. Based on these points we have to make cases.
1. If we take m<-10
The equation |m|>|m+10| becomes
-m>-m-10
0>-10 which satisfies the equation. So, for any m<-10, the equation satisfies. So, m+10, in this case, will be <0.
2. If we take -10<=m<0
The equation |m|>|m+10| becomes
-m>m+10
2m+10<0
m<-5
So, -10<=m<-5 satisfies the equation. So, m+10, in this case, will be >=0. It can be positive but then 0 also(neither positive nor negative)
We can see that we cannot get a unique answer. So, statement 1 is insufficient.
Statement 2: On the number line, m -10 is closer to 0 than to m.
Now, critical points for this equation are 10 and 0. Based on these points we have to make cases.
1. If we take m<0
The equation |m|>|m-10| becomes
-m>10-m
0>10 which does not satisfy the equation.
2. If we take 0<=m<10
The equation |m|>|m+10| becomes
m>10-m
2m-10>0
m>5
So, 5<m<10 satisfies the equation. So, m+10, in this case, will be >0.
3. If we take m>=10
The equation |m|>|m-10| becomes
m>m-10
0<10
So, m>=10 satisfies the equation. So, m+10, in this case, will be >0.
Thus, we see that m+10 will be positive in this case, we get a unique answer. Thus, Statement 2 is sufficient.
Thus, the answer is B
Is m+10 positive?
(1) On the number line, m+10 is closer to 0 than to m.
(2) On the number line, m -10 is closer to 0 than to m.
Solution:
Statement 1:On the number line, m+10 is closer to 0 than to m.
Now since this talks about the relative distance from 0, we can use modulus.
If I were to state Statment in mathematical terms, I would write |m|>|m+10|.
Now, critical points for this equation are -10 and 0. Based on these points we have to make cases.
1. If we take m<-10
The equation |m|>|m+10| becomes
-m>-m-10
0>-10 which satisfies the equation. So, for any m<-10, the equation satisfies. So, m+10, in this case, will be <0.
2. If we take -10<=m<0
The equation |m|>|m+10| becomes
-m>m+10
2m+10<0
m<-5
So, -10<=m<-5 satisfies the equation. So, m+10, in this case, will be >=0. It can be positive but then 0 also(neither positive nor negative)
We can see that we cannot get a unique answer. So, statement 1 is insufficient.
Statement 2: On the number line, m -10 is closer to 0 than to m.
Now, critical points for this equation are 10 and 0. Based on these points we have to make cases.
1. If we take m<0
The equation |m|>|m-10| becomes
-m>10-m
0>10 which does not satisfy the equation.
2. If we take 0<=m<10
The equation |m|>|m+10| becomes
m>10-m
2m-10>0
m>5
So, 5<m<10 satisfies the equation. So, m+10, in this case, will be >0.
3. If we take m>=10
The equation |m|>|m-10| becomes
m>m-10
0<10
So, m>=10 satisfies the equation. So, m+10, in this case, will be >0.
Thus, we see that m+10 will be positive in this case, we get a unique answer. Thus, Statement 2 is sufficient.
Thus, the answer is B
