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leeto
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 05:25
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

65% (02:44) correct 35% (02:48) wrong based on 123 sessions

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If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.
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C
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chetan2u
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Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
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GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,005
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 05:36
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leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.
Show more

Hi
+1 for a good Q..


lets solve now


\(a>b, a^2*b^2=144\) and \((a−b)^2=1\)
we know from \((a−b)^2=1\), a-b=1..

lets factorize 144 =2*2*2*2*3*3..
so a and b can be \(4^2*3^2 or (-3)^2*(-4)^2\)

lets check the statements now
I. a + b = 7
a+b=4+3=7 and
-3-4=-7
not NECESSARY

II. a - b = 1
4-3=1, and
-3-(-4)=1
Always TRUE

III. a - b = -1
NEVER true as can be seen from II

IV. ab = 12
4*3=12
(-3)(-4)=12
Always TRUE

V. ab = -12
Never true from above

so only II and IV are always true

ans C
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leeto
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 05:57
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chetan2u
leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.

Hi
+1 for a good Q..


lets solve now


\(a>b, a^2*b^2=144\) and \((a−b)^2=1\)
we know from \((a−b)^2=1\), a-b=1..

lets factorize 144 =2*2*2*2*3*3..
so a and b can be \(4^2*3^2 or (-3)^2*(-4)^2\)

lets check the statements now
I. a + b = 7
a+b=4+3=7 and
-3-4=-7
not NECESSARY

II. a - b = 1
4-3=1, and
-3-(-4)=1
Always TRUE

III. a - b = -1
NEVER true as can be seen from II

IV. ab = 12
4*3=12
(-3)(-4)=12
Always TRUE

V. ab = -12
Never true from above

so only II and IV are always true

ans C
Show more


Thx for kudos and for detail explanation ! Much appreciate !
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Bunuel
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Posts: 109,802
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 07:51
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leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.
Show more

What is the source of the question? GMAT questions does not have 5 must be true options (highlighted above) to choose from. The question cannot be from reliable GMAT source...
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leeto
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Posts: 17
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 08:10
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Bunuel
leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.

What is the source of the question? GMAT questions does not have 5 must be true options (highlighted above) to choose from. The question cannot be from reliable GMAT source...
Show more

Indeed you are right this is not from GMAT source. I thought it would be good idea to take a look on the GRE problems.
So I would this problem here : crunchprep.com GRE quantitative reasoning ( very hard level )
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Bunuel
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810,894
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 08:14
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leeto
Bunuel
leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.

What is the source of the question? GMAT questions does not have 5 must be true options (highlighted above) to choose from. The question cannot be from reliable GMAT source...

Indeed you are right this is not from GMAT source. I thought it would be good idea to take a look on the GRE problems.
So I would this problem here : crunchprep.com GRE quantitative reasoning ( very hard level )
Show more

Thank you. PS and DS sub-forums are for GMAT questions only. Please do not post GRE questions here.
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Bunuel
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Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,894
Given Kudos: 105,868
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GMAT Club Tests Forum Quiz
Expert
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
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If a and b are integers, a>b, a>b, a^2*b^2=144 and (a−b)^2=1 13 Mar 2016, 08:15
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leeto
Bunuel
leeto
If a and b are integers, \(a>b, a>b, a^2*b^2=144\) and \((a−b)^2=1\), which of the following MUST be true?

Indicate all such statements.

I. a + b = 7
II. a - b = 1
III. a - b = -1
IV. ab = 12
V. ab = -12

A) only I
B) only I & III
C) only II & IV
D) only IV & V
E) only III & V

Let's try to find most fastest way to solve this problem.

What is the source of the question? GMAT questions does not have 5 must be true options (highlighted above) to choose from. The question cannot be from reliable GMAT source...

Indeed you are right this is not from GMAT source. I thought it would be good idea to take a look on the GRE problems.
So I would this problem here : crunchprep.com GRE quantitative reasoning ( very hard level )
Show more
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