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If x and y are numbers such that x <  10 and y > 6, which of the
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Updated on: 07 Aug 2018, 06:15
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If x and y are numbers such that x <  10 and y > 6, which of the following expressions is true? I. x+4 +  y + 4 +  y4 + x – 4 > 32 II. x – 4 + y + 4   x + 4   y – 4 < 0 III. x + 4 + y + 4  x – 4  y – 4 = 0 (A) I only (B) II only (C) III only (D) I and III only (E) I, II and III This is Question 3 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. Happy Solving! Best Regards The eGMAT Team
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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22 May 2015, 07:17
Official ExplanationCorrect Answer: DFirst representing the points x and y on the number line: x < 10 and y > 6. Then, since the expressions talk about x+4, x4, y+4 and y4, representing these distances on the number line as well. x+4 represents the distance of x from 4 on the number line x4 represents the distance of x from 4 y+4 represents the distance of y from 4 y4 represents the distance of y from 4 I. x+4 +  y + 4 +  y4 + x – 4 > 32From the diagram it’s clear that: x+4 > 6 y + 4 >10 y – 4 > 2 x – 4 14 Adding all these we get Expression 1. Therefore, is true always. II. x – 4 + y + 4   x + 4   y – 4 < 0From the diagram, we can see that x – 4  x + 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x – 4 + y + 4   x + 4   y – 4 = 16 So, expression 2 is NOT TRUE. III. x + 4 + y + 4  x – 4  y – 4 = 0From the diagram, we can see that x + 4  x – 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x + 4 + y + 4  x – 4  y – 4 = 0 So, expression 3 is TRUE.
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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20 May 2015, 20:47
As stated, If x and y are numbers such that x <  10 and y > 6, if y > 6 , then  y + 4 = y + 4  y  4  = y  4 if x <  10 , then  x – 4  =  ( x – 4 )  x + 4 =  ( x + 4 ) lets solve each I. x+4 +  y + 4 +  y4 + x – 4 > 32 (x+4) + (y + 4) + (y  4)  (x – 4) > 32 x 4 + y + 4 + y  4 x +4 > 32 2x +2y > 32 x + y > 16 (10.1) + (6.1) > 16 ; True II. x – 4 + y + 4   x + 4   y – 4 < 0 (x4) + (y + 4)  ((x + 4))  (y4) < 0 x +4 + y + 4 +x 4 y +4 < 0 8 < 0 ; False III. x + 4 + y + 4  x – 4  y – 4 = 0 (x+4) + (y + 4)  ((x – 4))  (y  4) = 0 x 4 + y + 4 +x 4 y + 4 = 0 0 = 0 ; True Ans : D
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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20 May 2015, 14:26
Tried solving the question by substituting values for x and y. Suppose if we sub. x = 11 and y = 7, and solve the three equations, It's found that statements (i) and (iii) satisfy. Hence D.



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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21 May 2015, 11:51
EgmatQuantExpert wrote: If x and y are numbers such that x <  10 and y > 6, which of the following expressions is true? I. x+4 +  y + 4 +  y4 + x – 4 > 32 II. x – 4 + y + 4   x + 4   y – 4 < 0 III. x + 4 + y + 4  x – 4  y – 4 = 0 (A) I only (B) II only (C) III only (D) I and III only (E) I, II and III This is Question 3 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. The Official Answer and Explanation will be posted on 22nd May. Till then, Happy Solving! Best Regards The eGMAT Team How to solve this:Plug in smart values for x and y. The question tells us that x<10 and y>6. Therefore I take 11 = x and 7 = y. I. x+4 +  y + 4 +  y4 + x – 4 > 32 Plug in: 7 + 11 + 3 + 15 = 36 > 32 Be careful now, normally once you have an answer that is true, it doesn't mean that it will be true for all the values of x and y. Here im pretty confident because i took the smallest (integer) numbers for x and y and the result is 36 which is a difference of 4 to 32. Even if you plug in smaller fractional numbers the statement will still be true. II. x – 4 + y + 4   x + 4   y – 4 < 0 Plug in: 15 + 11  7  3 > 0, therefore false. No other plug ins are needed since one false value makes us eliminating it directly. III. x + 4 + y + 4  x – 4  y – 4 = 0 Plug in: 7 + 11  15  3 = 0, therefore true. But is it true for any values of x and y? What about y = 8 and x = 12? Let's try:Plug in #2: 8 + 12  16  4 = 0, obviously thats always true. Answer D like Dragon Any helpful recommendation how to do this in 2 minutes?
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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22 May 2015, 07:22
reto wrote: Any helpful recommendation how to do this in 2 minutes? Dear retoThe key to answering this question within 2 minutes is: the ability to represent x+4, x4, y+4, y4 on the number line. Do make sure that you are comfortable with this visual sense of absolute value. Best Regards Japinder
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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26 May 2015, 12:15
EgmatQuantExpert wrote: reto wrote: Any helpful recommendation how to do this in 2 minutes? Dear retoThe key to answering this question within 2 minutes is: the ability to represent x+4, x4, y+4, y4 on the number line. Do make sure that you are comfortable with this visual sense of absolute value. Best Regards Japinder To be honest, I feel more comfortable with plugging in. Just to set up the number line as you did in your example takes me too much time. And I don't feel comfortable with the number line, I assume that the error probability is bigger in my case by visualising the number line than plugging in.
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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05 Sep 2015, 00:12
EgmatQuantExpert wrote: If x and y are numbers such that x <  10 and y > 6, which of the following expressions is true? I. x+4 +  y + 4 +  y4 + x – 4 > 32 II. x – 4 + y + 4   x + 4   y – 4 < 0 III. x + 4 + y + 4  x – 4  y – 4 = 0 (A) I only (B) II only (C) III only (D) I and III only (E) I, II and III This is Question 3 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. Happy Solving! Best Regards The eGMAT Team but how do you confirm about this x – 4  x + 4 = 8 And, y + 4   y – 4 = 8 ???



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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16 Jul 2018, 08:16
EgmatQuantExpert wrote: Official ExplanationCorrect Answer: DFirst representing the points x and y on the number line: x < 10 and y > 6. Then, since the expressions talk about x+4, x4, y+4 and y4, representing these distances on the number line as well. x+4 represents the distance of x from 4 on the number line x4 represents the distance of x from 4 y+4 represents the distance of y from 4 y4 represents the distance of y from 4 I. x+4 +  y + 4 +  y4 + x – 4 > 32From the diagram it’s clear that: x+4 > 6 y + 4 >10 y – 4 > 2 x – 4 14 Adding all these we get Expression 1. Therefore, is true always. II. x – 4 + y + 4   x + 4   y – 4 < 0From the diagram, we can see that x – 4  x + 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x – 4 + y + 4   x + 4   y – 4 = 16 So, expression 2 is NOT TRUE. III. x + 4 + y + 4  x – 4  y – 4 = 0From the diagram, we can see that x + 4  x – 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x + 4 + y + 4  x – 4  y – 4 = 0 So, expression 3 is TRUE. What if non integers are considered? Will you solution work for that as well?



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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02 Nov 2018, 12:10
the image is not opening.



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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06 Nov 2018, 10:27
Unable to open the image in the solution. Can you please update the image.



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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18 Mar 2019, 12:19
Image is not opening. Can you please upload it again? EgmatQuantExpert



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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18 Mar 2019, 23:56
EgmatQuantExpert wrote: Official ExplanationCorrect Answer: DFirst representing the points x and y on the number line: x < 10 and y > 6. Then, since the expressions talk about x+4, x4, y+4 and y4, representing these distances on the number line as well. x+4 represents the distance of x from 4 on the number line x4 represents the distance of x from 4 y+4 represents the distance of y from 4 y4 represents the distance of y from 4 I. x+4 +  y + 4 +  y4 + x – 4 > 32From the diagram it’s clear that: x+4 > 6 y + 4 >10 y – 4 > 2 x – 4 14 Adding all these we get Expression 1. Therefore, is true always. II. x – 4 + y + 4   x + 4   y – 4 < 0From the diagram, we can see that x – 4  x + 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x – 4 + y + 4   x + 4   y – 4 = 16 So, expression 2 is NOT TRUE. III. x + 4 + y + 4  x – 4  y – 4 = 0From the diagram, we can see that x + 4  x – 4 = 8 And, y + 4   y – 4 = 8 Adding the 2 equations, we get: x + 4 + y + 4  x – 4  y – 4 = 0 So, expression 3 is TRUE. Can you please share the image of the number line? the one you have shared cant be open



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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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19 Mar 2019, 00:10
Hey everyone, We've taken a note of the image opening issue. Since it is an old post, we may take some time to update the diagram. We will update it soon.
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Re: If x and y are numbers such that x <  10 and y > 6, which of the
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14 Apr 2019, 00:41
Mohammad Ali Khan wrote: Can you please share the image of the number line? the one you have shared cant be open
Not sure how the actual image looked like. But I guess it would have looked something like this(attached below). Also, number substitution method of using smart numbers like x=11, y=7(discussed above) works faster than visualizing and over thinking on this number line diagram.
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Number line solution diagram.jpg [ 64.42 KiB  Viewed 1173 times ]
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If x and y are numbers such that x <  10 and y > 6, which of the
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13 Jul 2019, 03:11
EgmatQuantExpert wrote: Hey everyone,
We've taken a note of the image opening issue. Since it is an old post, we may take some time to update the diagram. We will update it soon. EgmatQuantExpert : Please share the image of the solution




If x and y are numbers such that x <  10 and y > 6, which of the
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13 Jul 2019, 03:11






