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For real numbers, A, B, C, and D on the number line [#permalink]
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04 Jan 2014, 23:57
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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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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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05 Jan 2014, 06:27
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. Answer: C. Hope it's clear.
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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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13 Jan 2015, 10:26
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



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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13 Jan 2015, 14:06
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. Your example: 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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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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14 Jan 2015, 06:34
Thank you Rich I got confused with the wording. But it make sense now. Appreciate it Regards Navdeep



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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28 Aug 2016, 13:29
Bunuel wrote: Notice that from the diagram we have that A<B<C<D. where does the diagram tell us that?



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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28 Aug 2016, 21:29
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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29 Aug 2016, 08:31
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?



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 09:15
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. OFFICIAL GUIDE:Problem SolvingFigures: 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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29 Aug 2016, 10:06
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. OFFICIAL GUIDE:Problem SolvingFigures: 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



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 10:55



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 11:12
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



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 11:19



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For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 11:49
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?



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Re: For real numbers, A, B, C, and D on the number line [#permalink]
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29 Aug 2016, 11:52
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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