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wickedvikram
Joined: 08 Jun 2008
Last visit: 28 Apr 2026
Posts: 195
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Location: India
Concentration: Finance, General Management
Schools: INSEAD Jan '26
GPA: 6.5
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24 Mar 2026, 02:36
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This question got me too. It asks integer value of Y and not X. for values of X such as 4.5, 3.5 ..... -3.5, -4.5 , Y will still be integer 
La1yaMalhotra
24 Mar 2026, 06:57
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If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?
y=|x+5|-|x-5|
Case 1: x <= -5
y = -x-5 - (5-x) = -x-5-5+x = -10
Case 2: -5 < x <= 5
y = x+5 - (5-x) = x+5-5+x = 2x
y = {-8,-6,-4,-2,0,2,4,6,8,10}
Case 3: x>5
y = x+5-(x-5) = x+5-x+5 = 10
Combining all above
y = {-10,-8,-6,-4,-2,0,2,4,6,8,10} : 21 values
IMO E
y=|x+5|-|x-5|
Case 1: x <= -5
y = -x-5 - (5-x) = -x-5-5+x = -10
Case 2: -5 < x <= 5
y = x+5 - (5-x) = x+5-5+x = 2x
y = {-8,-6,-4,-2,0,2,4,6,8,10}
Case 3: x>5
y = x+5-(x-5) = x+5-x+5 = 10
Combining all above
y = {-10,-8,-6,-4,-2,0,2,4,6,8,10} : 21 values
IMO E
