statement 1 seems to be INSUFF
consider x = 1/2, does satisfy x^2/|x| < 1
consider x = -2, does not satisfy x^2/|x| < 1
statement 2 seems to be INSUFF too
consider x = -1/2 and 2, the later does not satisfy x^2/|x| < 1
statement 1 and statement 2
-1 < x < 1 seems to satisfy x^2/|x| < 1
I think the answer should be C
Whats the OA?
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absolute value
Source: Beat The GMAT — Data Sufficiency |
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Stuart@KaplanGMAT
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Let's start by simplifying the question.beater wrote:If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1
Is x^2/|x|< 1?
Well, we know that |x| is positive (since x ≠ 0), so it's safe to multiply both sides by |x| to get:
is x^2 < |x|?
When is the square of a number less than the number itself? If x is a positive fraction. Since in this question it's less than the abolute value of the number itself, a negative fraction will work as well.
So, the question really is: Is x a positive or negative fraction?
(1) x < 1
Could be a fraction, could be a negative non-fraction: insufficient.
(2) x > -1
Could be a fraction, could be a positive non-fraction: insufficient.
Combined:
-1 < x < 1
Well, the only numbers in that range are fractions and 0. Since x ≠ 0, x MUST be a fraction: sufficient.
Together the statements are sufficient even though independently they're not: choose (C).
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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Stuart,
I picked numbers and determined the answer to be C.
I am really confused when mod functions appear. You said |x| is positive (since x ≠ 0)
Is mod 0 undefined since we cant apply the mod rule
mod x = x if x is positive
mod x = -x if x is negative
I habe 2 other mod problems that I was confused on based on explanations given. Iknew I coudnt ask those questiosn here since I would mixing up this thread.
I may have to open 2 new threads for these.
Thanks agian for youer explanations (Always use the Pascals triangle approach of yours when it comes to problem where the prob is 1/2
)
I picked numbers and determined the answer to be C.
I am really confused when mod functions appear. You said |x| is positive (since x ≠ 0)
Is mod 0 undefined since we cant apply the mod rule
mod x = x if x is positive
mod x = -x if x is negative
I habe 2 other mod problems that I was confused on based on explanations given. Iknew I coudnt ask those questiosn here since I would mixing up this thread.
I may have to open 2 new threads for these.
Thanks agian for youer explanations (Always use the Pascals triangle approach of yours when it comes to problem where the prob is 1/2
)-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
|0| = 0cramya wrote:Stuart,
I picked numbers and determined the answer to be C.
I am really confused when mod functions appear. You said |x| is positive (since x ≠ 0)
Is mod 0 undefined since we cant apply the mod rule
mod x = x if x is positive
mod x = -x if x is negative
I habe 2 other mod problems that I was confused on based on explanations given. Iknew I coudnt ask those questiosn here since I would mixing up this thread.
I may have to open 2 new threads for these.
Thanks agian for youer explanations (Always use the Pascals triangle approach of yours when it comes to problem where the prob is 1/2
Absolute value measures the distance between what's inside the brackets and 0 on the number line. The distance from 0 to 0 is... 0!
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
hello stuartStuart Kovinsky wrote:Let's start by simplifying the question.beater wrote:If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1
Is x^2/|x|< 1?
Well, we know that |x| is positive (since x ≠ 0), so it's safe to multiply both sides by |x| to get:
is x^2 < |x|?
When is the square of a number less than the number itself? If x is a positive fraction. Since in this question it's less than the abolute value of the number itself, a negative fraction will work as well.
So, the question really is: Is x a positive or negative fraction?
(1) x < 1
Could be a fraction, could be a negative non-fraction: insufficient.
(2) x > -1
Could be a fraction, could be a positive non-fraction: insufficient.
Combined:
-1 < x < 1
Well, the only numbers in that range are fractions and 0. Since x ≠ 0, x MUST be a fraction: sufficient.
Together the statements are sufficient even though independently they're not: choose (C).
Can you please clarify how |x| is +ve, if x!=0
Thanks in advance
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
By definition, the absolute value of a number is the distance between that number and 0 on the number line.hello stuart
Can you please clarify how |x| is +ve, if x!=0
If x is not equal to 0, the distance from x to 0 will always be positive.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1[/quote]
Absolute value is nothing but a distance. How far is something from 0 ?
So question asks whether square of an integer is smaller than its distance to 0.
Well we know that this can not be a positive number greater than 1
But we also know that numbers act FUNNY between the GMAT zone 0 and 1
Since the numbers get smaller between 0-1 we have to find this piece of information in the answers. Actually the same thing applies to numbers between -1 and 0 in this case because of the absolute value.
So actually the range we are looking for is:
-1<x<0
0>x>1
Remember 0 can not be a solution so
-1<x<1 where x ≠ 0
(C)
(1) x < 1
(2) x > −1[/quote]
Absolute value is nothing but a distance. How far is something from 0 ?
So question asks whether square of an integer is smaller than its distance to 0.
Well we know that this can not be a positive number greater than 1
But we also know that numbers act FUNNY between the GMAT zone 0 and 1
Since the numbers get smaller between 0-1 we have to find this piece of information in the answers. Actually the same thing applies to numbers between -1 and 0 in this case because of the absolute value.
So actually the range we are looking for is:
-1<x<0
0>x>1
Remember 0 can not be a solution so
-1<x<1 where x ≠ 0
(C)
LGTCH
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Hi Ian,
I am looking for an algebric soln to these absolutes, is that possible.
Regards,
maihuna
I am looking for an algebric soln to these absolutes, is that possible.
Regards,
maihuna
