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# M26-12

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 00:25
13
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:14) correct 36% (01:02) wrong based on 223 sessions

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If $$-3 \lt x \lt 5$$ and $$-7 \lt y \lt 9$$, which of the following represents the range of all possible values of $$y-x$$?

A. $$-4 \lt y-x \lt 4$$
B. $$-2 \lt y-x \lt 4$$
C. $$-12 \lt y-x \lt 4$$
D. $$-12 \lt y-x \lt 12$$
E. $$4 \lt y-x \lt 12$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 00:25
1
3
Official Solution:

If $$-3 \lt x \lt 5$$ and $$-7 \lt y \lt 9$$, which of the following represents the range of all possible values of $$y-x$$?

A. $$-4 \lt y-x \lt 4$$
B. $$-2 \lt y-x \lt 4$$
C. $$-12 \lt y-x \lt 4$$
D. $$-12 \lt y-x \lt 12$$
E. $$4 \lt y-x \lt 12$$

To get max value of $$y-x$$ take max value of $$y$$ and min value of $$x$$: $$9-(-3)=12$$;

To get min value of $$y-x$$ take min value of $$y$$ and max value of $$x$$: $$-7-(5)=-12$$;

Hence, the range of all possible values of $$y-x$$ is $$-12 \lt y-x \lt 12$$.

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Joined: 06 Mar 2014
Posts: 239
Location: India
GMAT Date: 04-30-2015

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16 Sep 2014, 09:42
1
Bunuel wrote:
Official Solution:

If $$-3 \lt x \lt 5$$ and $$-7 \lt y \lt 9$$, which of the following represents the range of all possible values of $$y-x$$?

A. $$-4 \lt y-x \lt 4$$
B. $$-2 \lt y-x \lt 4$$
C. $$-12 \lt y-x \lt 4$$
D. $$-12 \lt y-x \lt 12$$
E. $$4 \lt y-x \lt 12$$

To get max value of $$y-x$$ take max value of $$y$$ and min value of $$x$$: $$9-(-3)=12$$;

To get min value of $$y-x$$ take min value of $$y$$ and max value of $$x$$: $$-7-(5)=-12$$;

Hence, the range of all possible values of $$y-x$$ is $$-12 \lt y-x \lt 12$$.

This question is good but it would be interesting to see a question with the same guidelines as to find the range of values but with the variables x/y or both with inclusive numbers like -3<=x<5 and -7<y<=9.

Also if possible, kindly suggest similar problems.
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 13:32
1
earnit wrote:
Bunuel wrote:
Official Solution:

If $$-3 \lt x \lt 5$$ and $$-7 \lt y \lt 9$$, which of the following represents the range of all possible values of $$y-x$$?

A. $$-4 \lt y-x \lt 4$$
B. $$-2 \lt y-x \lt 4$$
C. $$-12 \lt y-x \lt 4$$
D. $$-12 \lt y-x \lt 12$$
E. $$4 \lt y-x \lt 12$$

To get max value of $$y-x$$ take max value of $$y$$ and min value of $$x$$: $$9-(-3)=12$$;

To get min value of $$y-x$$ take min value of $$y$$ and max value of $$x$$: $$-7-(5)=-12$$;

Hence, the range of all possible values of $$y-x$$ is $$-12 \lt y-x \lt 12$$.

This question is good but it would be interesting to see a question with the same guidelines as to find the range of values but with the variables x/y or both with inclusive numbers like -3<=x<5 and -7<y<=9.

Also if possible, kindly suggest similar problems.

Here is a similar questions with equal signs: if-2-x-2-and-3-y-8-which-of-the-following-represents-the-73539.html
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19 Sep 2015, 03:50
3
1
Hi

another approach: sum up the 2 inequalities. but mind that the inequalities for such operaton should be looking the same way.

since we need to find y-x, we need to figure out how to transform the x-inequality into the required form, i.e. -x:
1. multiply by (-1): we get +3>-x>-5 (remember to flip direction when * -1)
2. still is not looking the same way, therefore: -5<-x<3 is just the same expression of the number line fragment

3. sum-up:
-7 < y <9
-5 <-x <3
-----------------
-7-5 < y-x < 9+3
-12 < y-x< 12

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KUDO me plenty

Intern
Joined: 24 Nov 2015
Posts: 1

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01 Jan 2016, 20:01
1
The questions states that the values are less than or greater than. but the answer explanation uses values that are greater than or EQUAL TO!! The explanation uses values that are not in the range of values given in the question
Intern
Joined: 17 Oct 2015
Posts: 21

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03 Mar 2016, 16:35
The same for me.. Is the OE wrong?

weiling476 wrote:
The questions states that the values are less than or greater than. but the answer explanation uses values that are greater than or EQUAL TO!! The explanation uses values that are not in the range of values given in the question
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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07 Mar 2016, 09:41
1
1
mestrec wrote:
The same for me.. Is the OE wrong?

weiling476 wrote:
The questions states that the values are less than or greater than. but the answer explanation uses values that are greater than or EQUAL TO!! The explanation uses values that are not in the range of values given in the question

The OE is correct.

Consider the following approach, we have -3<x<5 and -7<y<9,

Add y<9 and -3<x --> y-3<9+x --> y-x<12;
Add -7<y and x<5 --> -7+x<y+5 --> -12<y-x;

So, we have that -12<y-x<12.

Hope it's clear.
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06 Apr 2016, 00:29
I don't agree with the explanation. If x is less than 9 then maximum value of x is 8. similarly for Y. kindly explain why maximum value for x is 9.
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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06 Apr 2016, 00:38
Ratnam123 wrote:
I don't agree with the explanation. If x is less than 9 then maximum value of x is 8. similarly for Y. kindly explain why maximum value for x is 9.

Kindly check the discussion above. I think your doubts are addressed there. Ask if anything remains unclear.
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07 Jan 2017, 10:48
Bunuel,

I'm not doubting the question itself, but when other people raised issues about the explanation, i think it's reasonable to doubt why the maximum VALUE of y is 9, and minimum VALUE of x is -3. Your wording is totally misguiding. You should say the maximum RANGE of y, rather than the value. The maximum value in this case is not 9, it's 8.99. Since the question is saying that the range is <>, not <=,>=.
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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08 Jan 2017, 04:49
conneryeon001 wrote:
Bunuel,

I'm not doubting the question itself, but when other people raised issues about the explanation, i think it's reasonable to doubt why the maximum VALUE of y is 9, and minimum VALUE of x is -3. Your wording is totally misguiding. You should say the maximum RANGE of y, rather than the value. The maximum value in this case is not 9, it's 8.99. Since the question is saying that the range is <>, not <=,>=.

The question and the solution are absolutely correct. I think your doubt is addressed here: m26-184451.html#p1655617

Hope it helps.
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21 Apr 2017, 00:36
I think a much simpler way to solve this problem is to simply subtract two inequlities, according to the inequalities subtraction rules: (-7<y<9)-(5>x>-3) <----last inequality simply reversed. And we get the same answer -12<y-x<12
Manager
Joined: 23 Jun 2016
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09 Nov 2017, 18:12
(1) -3<x<5
(2) -7<y<9

I made a mistake and subtracted (1) from (2) (since signs are similar in two statements) giving
-4 < (y-x) < 4

I agree with the OE but can someone explain if the above allowed and if yes what information does it convey?
Math Expert
Joined: 02 Aug 2009
Posts: 7204

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09 Nov 2017, 18:46
1
sevenplusplus wrote:
(1) -3<x<5
(2) -7<y<9

I made a mistake and subtracted (1) from (2) (since signs are similar in two statements) giving
-4 < (y-x) < 4

I agree with the OE but can someone explain if the above allowed and if yes what information does it convey?

No, it is wrong and you can simply test it with numbers..

(1) -3<x<5 ......let x be the lowest possible -2.99999
(2) -7<y<9 ...... let y be the MAX, so 8.99999
y-x = 8.99999-(-2.99999) = 10 and 10 is not in the range -4<y-x<4

you can ofcourse ADD the equations..

(1) -3<x<5
(2) -7<y<9
so -3+(-7)<x+y<5+9......-10<x+y<14

so to sum it all
2) If you are subtracting, take highest of one and lowest of other
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 23 Jun 2016
Posts: 98

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11 Nov 2017, 10:17
chetan2u wrote:
sevenplusplus wrote:
(1) -3<x<5
(2) -7<y<9

I made a mistake and subtracted (1) from (2) (since signs are similar in two statements) giving
-4 < (y-x) < 4

I agree with the OE but can someone explain if the above allowed and if yes what information does it convey?

No, it is wrong and you can simply test it with numbers..

(1) -3<x<5 ......let x be the lowest possible -2.99999
(2) -7<y<9 ...... let y be the MAX, so 8.99999
y-x = 8.99999-(-2.99999) = 10 and 10 is not in the range -4<y-x<4

you can ofcourse ADD the equations..

(1) -3<x<5
(2) -7<y<9
so -3+(-7)<x+y<5+9......-10<x+y<14

so to sum it all
2) If you are subtracting, take highest of one and lowest of other

Thanks a ton.

Sent from my iPhone using GMAT Club Forum mobile app
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27 May 2018, 14:10
Bunuel wrote:
If $$-3 \lt x \lt 5$$ and $$-7 \lt y \lt 9$$, which of the following represents the range of all possible values of $$y-x$$?

A. $$-4 \lt y-x \lt 4$$
B. $$-2 \lt y-x \lt 4$$
C. $$-12 \lt y-x \lt 4$$
D. $$-12 \lt y-x \lt 12$$
E. $$4 \lt y-x \lt 12$$

Can be solved in less than 20 secs by looking at the answer choices. Since each answer choice has y-x in the middle, we can directly compare the min and max values across the different answer choices. The range of choice D covers all of the other ranges. This means that if any choice besides D is correct, then D would also be correct, but we cant have 2 right answers, so answer is D.
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22 Jul 2018, 00:26
Bunuel,
Hi Bunuel,
Would you mind sharing an explanation by plotting on line, if possible?
Thanks!
Re: M26-12 &nbs [#permalink] 22 Jul 2018, 00:26
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# M26-12

Moderators: chetan2u, Bunuel

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