A set contains the following 5 numbers:
a^2,a^5,a,a/2, and a/5
Is the range of the set equal to a^2-a^5 ?
a is negative
a^5<a
Is the range of the set equal to a^2–a^5 ?
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- ygdrasil24
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I. Since a is <0, a2 will be max and a5 will be least hence range is a2-a5. SO A is sufficienthimu wrote:A set contains the following 5 numbers:
a^2,a^5,a,a/2, and a/5
Is the range of the set equal to a^2-a^5 ?
a is negative
a^5<a
II. a5<a , implies a < 0 , so like statement I, B is sufficient.
Hence Answer is C
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- Atekihcan
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The question is simply asking whether a² and a� are the largest and smallest among the five numbers, respectively.
Now, whenever comparison of powers of a variable is involved always consider positive and negative values as well as values greater than and smaller than 1 and -1.
Statement 1: a < 0
If a = -2.0, a² is largest and a� is smallest ---> YES
If a = -1/2, a² is largest and a is smallest ---> NO
So, statement 1 is not sufficient
Statement 2: a� < a
So either a < -1 or 0 < a < 1
If a = -2.0, a² is largest and a� is smallest ---> YES
If a = 1/2, a is largest and a� is smallest ---> NO
So, statement 2 is not sufficient
Both statements together: a < -1
So, a² is largest and a� is smallest ---> YES
So, both statements together is sufficient
Answer : C
Now, whenever comparison of powers of a variable is involved always consider positive and negative values as well as values greater than and smaller than 1 and -1.
Statement 1: a < 0
If a = -2.0, a² is largest and a� is smallest ---> YES
If a = -1/2, a² is largest and a is smallest ---> NO
So, statement 1 is not sufficient
Statement 2: a� < a
So either a < -1 or 0 < a < 1
If a = -2.0, a² is largest and a� is smallest ---> YES
If a = 1/2, a is largest and a� is smallest ---> NO
So, statement 2 is not sufficient
Both statements together: a < -1
So, a² is largest and a� is smallest ---> YES
So, both statements together is sufficient
Answer : C
- ygdrasil24
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@ Atekihcan
Statement 1: a < 0
If a = -1/2, a² is largest and a is smallest ---> NO
Was it not supposed to be a^5 in the above case ?
Statement 1: a < 0
If a = -1/2, a² is largest and a is smallest ---> NO
Was it not supposed to be a^5 in the above case ?
- Atekihcan
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If a = -1/2, a^5 = -1/32 > -1/2burningman wrote:If a = -1/2, a² is largest and a is smallest ---> NO
Was it not supposed to be a^5 in the above case ?
So, a is the smallest not a^5