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Intern  Joined: 21 Mar 2013
Posts: 38
GMAT Date: 03-20-2014
For real numbers, A, B, C, and D on the number line  [#permalink]

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34 00:00

Difficulty:   95% (hard)

Question Stats: 40% (02:15) correct 60% (02:03) wrong based on 407 sessions

HideShow timer Statistics For real numbers, A, B, C, and D on the number line above, is |A| + |B| < |C| + |D| ?

(1) |B| < |C|
(2) The product of any two of the numbers A, B, C and D is between 0 and 1.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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9
5 For real numbers, A, B, C, and D on the number line above, is |A| + |B| < |C| + |D| ?

Notice that from the diagram we have that A<B<C<D.

(1) |B| < |C|. This one is clearly insufficient. Consider: A=1, B=2, C=3, and D=4 for an YES answer and A=-10, B=2, C=3, and D=4 for a NO answer. Not sufficient.

(2) The product of any two of the numbers A, B, C and D is between 0 and 1. So, we have that the product of ANY two of the numbers is positive. This implies either that all the numbers are negative or that all the numbers are positive. In the first case the answer is NO and in the second case the answer is YES. Not sufficient.

(1)+(2) If all the numbers were negative, then because we also have that B < C, then we would have that |B| > |C|, which contradicts the first statement, thus we have the second case: all the numbers are positive. Therefore since A<B<C<D, then |A| + |B| < |C| + |D|. Sufficient.

Hope it's clear.
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Intern  Joined: 25 Feb 2013
Posts: 7
GMAT Date: 12-22-2014
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Bunuel wrote:

(2) The product of any two of the numbers A, B, C and D is between 0 and 1. So, we have that the product of ANY two of the numbers is positive. This implies either that all the numbers are negative or that all the numbers are positive. In the first case the answer is NO and in the second case the answer is YES. Not sufficient.

Hi Bunuel,

I have been reading your posts quite regularly, and they are very helpful. I am really grateful to you for providing assistance to people like us.

As far as this question is concerned i have a doubt on s(2). As you have mentioned above "that all the numbers are negative or that all the numbers are positive."
I have been working on one or two examples and came across this one
Suppose B and C are -1/2 and -1/3. Their product is 1/6, which is between 0 and 1. Now the possible values can be
A<B<C<D :- -1 < -1/2 < -1/3 <1 . In this case |A| + |B| IS NOT LESS THAN |C| + |D| insufficient

Suppose A and B are -1/2 and -1/3. Again their product is 1/6, which is between 0 and 1. Now the possible values can be
A<B<C<D :- -1/2 < -1/3 < 1 < 2. In this case |A| + |B| < |C| + |D| sufficient.

So, how can we say "that all the numbers are negative or that all the numbers are positive." ? and it doesn't say that The product of every two of the numbers A, B, C and D is between 0 and 1.

Thanks
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Hi pahujanavdeep,

Unfortunately, your example does NOT fit the "restriction" that is described in Fact 2:

Fact 2: The product of any two of the numbers A, B, C and D is between 0 and 1.

This tells us that if we take ANY two of the 4 values and multiply them....then the product will be a POSITIVE fraction.

A = -1
B = -1/2
C = -1/3
D = 1

If one of the two numbers chosen is D, then the product will be a NEGATIVE fraction. This is NOT a viable option given what Fact 2 tells us. The ONLY ways for the product of ANY two of those values to be a POSITIVE fraction is if ALL 4 values are negative OR ALL 4 are positive.

GMAT assassins aren't born, they're made,
Rich
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Intern  Joined: 25 Feb 2013
Posts: 7
GMAT Date: 12-22-2014
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Thank you Rich I got confused with the wording. But it make sense now. Appreciate it Regards
Navdeep
Manager  Joined: 22 Sep 2015
Posts: 88
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Bunuel wrote: Notice that from the diagram we have that A<B<C<D.

where does the diagram tell us that?
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich
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Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich

so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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1
nycgirl212 wrote:
EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich

so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?

Please check the highlighted part below.

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
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Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Bunuel wrote:
nycgirl212 wrote:
EMPOWERgmatRichC wrote:
Hi nycgirl212,

The prompt specifically refers to the number line that's presented. On a number line, numbers increase from left to right. Thus, based on the given number line, A < B < C < D.

GMAT assassins aren't born, they're made,
Rich

so even though it doesn't explicitly state that the numbers increase from left to right, we are automatically supposed to assume that they do when we see a number line?

Please check the highlighted part below.

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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nycgirl212 wrote:

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand

That's a common knowledge.
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Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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Bunuel wrote:
nycgirl212 wrote:

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand

That's a common knowledge.

Obviously, the question was more of can i assume that a line shows in a diagram will always reflect those properties
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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nycgirl212 wrote:
Bunuel wrote:
nycgirl212 wrote:

thanks, but where does it say that all numbers in a number line increase from left to right? I'm just trying to understand

That's a common knowledge.

Obviously, the question was more of can i assume that a line shows in a diagram will always reflect those properties

I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear above?
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Manager  Joined: 22 Sep 2015
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For real numbers, A, B, C, and D on the number line  [#permalink]

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Bunuel wrote:
I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear above?

the question is when I see a diagram like this on a GMAT question, can i automatically assume the numbers increase from left to right and are not just randomly assigned (i.e. A is 10, B is -5, C is 20, D is 4)? Yes or no? Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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nycgirl212 wrote:
Bunuel wrote:
I don't understand what you mean...

1. On a number line, numbers increase from left to right - that's a common knowledge;
2. The positions of points, on a diagram exist in the order shown - that's according to the GMAC.

Hence, A < B < C < D.

What is unclear above?

the question is when I see a diagram like this on a GMAT question, can i automatically assume the numbers increase from left to right and are not just randomly assigned (i.e. A is 10, B is -5, C is 20, D is 4)? Yes or no? ________________________
Yes...
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Re: For real numbers, A, B, C, and D on the number line  [#permalink]

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_________________ Re: For real numbers, A, B, C, and D on the number line   [#permalink] 13 Oct 2018, 04:40
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