If x and y are two integers, and 1

Question

If x and y are two integers, and 1 < x + 3 < 8 and 7 < 3 - y < 20, what is the maximum possible value of x + y?

A. -1
B. 0
C. 1
D. 5
E. 20

Why not the answer is 20? if I  multiply y with -1 , it is supposed to be 20.

Bunuel · Accepted Answer

1 < x + 3 < 8

Add -3 to get -2 < x < 5
So, the maximum possible value of x is 4.

7 < 3 - y < 20

Multiply by -1 and flip the signs:
-7 > y - 3 > -20
Add 3: to get -4 > y > -17
So, the maximum possible value of y is -5.

Thus, the maximum possible value of x + y is 4 + (-5) = -1.

Answer: A.

Strategix · Answer

Edited to account for integer restriction

Option A.

From 1 we get: -2 < x < 5
 
From 2 we get: -17 < y < -4

Minimum:x + y = -17
Maximum: x + y = -1

ravi1522 · Answer

Hello ,

From 1 we get: -2 < x < 5

From 2 we get: -17 < y < -4

-17 < X+Y < 1
As it is integer so max value will be 0.

Hence Option B.

findingmyself · Answer

1<x<5
Possible values of X=(2,3,4)

7<3-y<20
Minimum value satisfying this is -5
Range is (-5,-6,.....-16)

Max" 4-5=-1

argha3110 · Answer

The answer should be -1 right?

Ayeka · Answer

Yes answer is -1 1 < x + 3 < 8 1-3 < x < 8-3 ; -2y>-17 maximum possible value of x + y = 4-5=-1

nguyen11223344 · Answer

why the answer is C guy?

Kinshook · Answer

If x and y are two integers, and 1 < x + 3 < 8 and 7 < 3 - y < 20, what is the maximum possible value of x + y?

-2 < x < 5
4 < -y < 17
-17 < y < -4

-2-17 < x+y < 5-4 
-19 < x + y < 1

Maximum value of x = 4
Maximum value of y = -5
Maximum value of x+y = 4 - 5 = - 1

IMO A

Kinshook · Answer

Bunuel

-2 < x < 5
-17 < y < -4
-19 < x+y < 1

But there is no equal sign in inequalities, 
Max x+y can not be 1 but can be 0.

Please recheck OA & OE.

Bunuel · Answer

You are missing a point. We are given that x and y are integers.

From -2 < x < 5, the maximum possible value of x is 4.
From -4 > y > -17, the maximum possible value of y is -5.

Thus, the maximum possible value of x + y is 4 + (-5) = -1.

agrasan · Answer

Hi  Bunuel 
The question shows answer as (C), can we please correct that? I agree with the method that answer is -1 only.

Bunuel · Answer

_____________________________

Fixed the OA. Thank you!

IAMFORCR · Answer

Why is this approach wrong ??

Bunuel · Answer

It misses the fact that x and y are restricted to integers.

IAMFORCR · Answer

I appreciate your reply and think this approach is wrong but i do not see how that is a problem.

Krunaal · Answer

The problem is that there  won't be valid values for x and y  that give x + y = 0

If x and y are two integers, and 1 < x + 3 < 8 and 7 < 3 - y < 20

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