If ab ≠0, is ab > a/b ?
(1) |b| > 1
(2) ab + a/b > 0
Guys ,
Our target question is ab>a/b
we can rephrase and get b^2>1
Statement 1- |b|>1
this means b>1 or b<-1 right?
so statement 1 is sufficient right?
Pls correct me and explain me really need help...
ab>a/b
This topic has expert replies
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
ab > a/b?If ab ≠0, is ab > a/b ?
(1) |b| > 1
(2) ab + a/b > 0
ab - a/b > 0
ab²/b - a/b > 0
(ab² - a) / b > 0
[ (a)(b² - 1) ] / b > 0
(a/b)(b² - 1) > 0?
Question stem, rephrased: Are a/b and b² - 1 the SAME SIGN?
Statement 1: |b| > 1
Thus, b² - 1 > 0.
No information about a/b.
INSUFFICIENT.
Statement 2: ab + a/b > 0
ab²/b + a/b > 0
(ab² + a) / b > 0
[ (a)(b² + 1) ] / b > 0
(a/b)(b² + 1) > 0.
Since it is not possible for b² + 1 to be negative, the inequality above holds true only if a/b > 0.
No information about b² - 1.
INSUFFICIENT.
Statements combined:
Statement 1: b² - 1 > 0.
Statement 2: a/b > 0.
Thus, a/b and b² - 1 are the SAME SIGN.
SUFFICIENT.
The correct answer is C.
When an inequality is multiplied or divided by a negative value, the direction of the inequality must FLIP.Our target question is ab>a/b
we can rephrase and get b^2>1
Here, the signs of a and b are unknown.
Thus, if we multiply each side by b and divide each side by a, we cannot be certain whether the resulting inequality should be b²>1 or b²<1.
For this reason, it is safer to eschew algebra or to simplify as I did in my solution above.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
Thanks Guru for your explanation it helps a lot, one more thing which i need to be cleared.
What else should be given in the question so that i can rephrase my target question from ab>a/b to b^2>1.
What else should be given in the question so that i can rephrase my target question from ab>a/b to b^2>1.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
If the question stem indicated that ab > 0, then we could rephrase ab > a/b as b² > 1.j_shreyans wrote:Thanks Guru for your explanation it helps a lot, one more thing which i need to be cleared.
What else should be given in the question so that i can rephrase my target question from ab>a/b to b^2>1.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi j_shreyans,
"Rewriting" a DS question can be a rather useful tactic on Test Day (in certain circumstances). You have to decide two things though before (and sometimes after) you try to rewrite the question:
1) Do you know the math rules perfectly, so that you don't make a mistake?
2) Is the "new" question easier for you to deal with than the original question?
Here, we're told that A and B CANNOT = 0. We're asked if AB > A/B? This is a YES/NO question.
*Of all the various calculations that the GMAT might ask you to perform, multiplying 2 numbers and dividing 2 numbers are relatively simple tasks, so I'm not going to try to change this question at all.*
Since there are variables, this looks like a great opportunity to TEST VALUES and use some Number Properties to your advantage.
Fact 1: |B| > 1
Here, we have some minor restrictions on the the value of B, but no restrictions on A (other than the fact that it can't be 0)
If...
A = 1
B = 2
(1)(2) > 1/2 and the answer to the question is YES
A = 1
B = -2
1(-2) is NOT > 1/-2 and the answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: AB + A/B > 0
Here, we can use the first TEST from Fact 1....
A = 1
B = 2
The answer to the question is YES.
If...
A = 1
B = 1
The answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know:
|B| > 1
AB + A/B > 0
Using Number Properties, we can deduce that....
B > 1 OR B < -1
If B is Negative, then A MUST be Negative (which would make AB + A/B > 0)
If B is Positive, then A MUST be Positive (which would make AB + A/B > 0)
So A and B MUST have the SAME SIGN.
With the restrictions on B, multiplying A by B will lead to a BIGGER VALUE; and dividing A by B lead to a SMALLER VALUE. Thus AB will ALWAYS > A/B. The answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
"Rewriting" a DS question can be a rather useful tactic on Test Day (in certain circumstances). You have to decide two things though before (and sometimes after) you try to rewrite the question:
1) Do you know the math rules perfectly, so that you don't make a mistake?
2) Is the "new" question easier for you to deal with than the original question?
Here, we're told that A and B CANNOT = 0. We're asked if AB > A/B? This is a YES/NO question.
*Of all the various calculations that the GMAT might ask you to perform, multiplying 2 numbers and dividing 2 numbers are relatively simple tasks, so I'm not going to try to change this question at all.*
Since there are variables, this looks like a great opportunity to TEST VALUES and use some Number Properties to your advantage.
Fact 1: |B| > 1
Here, we have some minor restrictions on the the value of B, but no restrictions on A (other than the fact that it can't be 0)
If...
A = 1
B = 2
(1)(2) > 1/2 and the answer to the question is YES
A = 1
B = -2
1(-2) is NOT > 1/-2 and the answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: AB + A/B > 0
Here, we can use the first TEST from Fact 1....
A = 1
B = 2
The answer to the question is YES.
If...
A = 1
B = 1
The answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know:
|B| > 1
AB + A/B > 0
Using Number Properties, we can deduce that....
B > 1 OR B < -1
If B is Negative, then A MUST be Negative (which would make AB + A/B > 0)
If B is Positive, then A MUST be Positive (which would make AB + A/B > 0)
So A and B MUST have the SAME SIGN.
With the restrictions on B, multiplying A by B will lead to a BIGGER VALUE; and dividing A by B lead to a SMALLER VALUE. Thus AB will ALWAYS > A/B. The answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich