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# x and y are integers. x + y < 11 , and x > 6. What is the smallest pos

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x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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13 May 2016, 05:00
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35% (medium)

Question Stats:

68% (01:31) correct 32% (01:39) wrong based on 197 sessions

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x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?

A. 1
B. 2
C. 4
D. -2
E. -4

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Posts: 375
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
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x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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13 May 2016, 13:50
1
Constraints: X>6, x,y are integers (no fractions) and x+y<11 (can be positive or negative)

Test Case 1: X and Y are positive:
X(>6) Y(positive integer) X+Y<11 X-Y
7 3 10 4
8 2 10 6
9 1 10 8
10 0 0 10

Least difference in the above is 4

Test Case 2 : X is positive Y is negative:

X(>6) Y(positive integer) X+Y<11 X-Y
7 -8 -1 15
8 -7 1 15
9 -6 3 15
10 -4 6 14

Least Difference X-Y as you can is far higher when Y is negative. Hence test case 2 is rules out , going by test case 1 and other constraints defined in the problem only answer is Least difference in the above is Choice C- 4
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Re: x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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06 Jun 2016, 21:46
1
Bunuel wrote:
x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?

A. 1
B. 2
C. 4
D. -2
E. -4

Because x & y are integers, the two equations can be simply written as :
x+y<= 10 --- eq. 1
x>= 7 ---- eq. 2

For smallest value of x-y, x has to be the smallest whereas y has to be the largest.
From the above eq. 2, smallest value of x = 7
Plugging it in eq. 1: 7+y<=10, or y<=3
Therefore, largest value of y=3 & smallest values of x=7
x-y = 7 - 3 = 4
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Re: x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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06 Jun 2016, 23:03
2
2
Bunuel wrote:
x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?

A. 1
B. 2
C. 4
D. -2
E. -4

Focus on the transition points and plug in the values.
x > 6 so x could be 7, 8, 9, 10, 11 etc

Look at x = 7
7 + y < 11
y < 4
y could be 3, 2, 1, 0, -1 etc
When y is 3, we get x - y = 4

This must be the smallest value because as x increases, y reduces so x - y increases.
Take another example. x = 11 so y < 0.
x - y will give a value greater than 11.

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Re: x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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06 Jun 2016, 23:43
Bunuel wrote:
x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?

A. 1
B. 2
C. 4
D. -2
E. -4

Smallest value of x-y will be obtained when x and y are nearest to one another.

x > 6. This means that for x-y to be negative value y has to be more than 7. in such a situation x+y cannot be less than 11.

So D and E are out.

Now if negative value is not there, next best option is zero. x+y< 11. Say x=y=5, then x+y = 10 which is less than 11.

But x has to more than 6.

So: values of x = 7, 8, 9 , 10. Then values of y 3, 2, 1 and 0

Smallest value of x-y will be obtained when x and y are nearest to one another.

smallest difference will be 4. (any effort to reduce this difference below 4 will not be possible and will negate x+y <11.

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Re: x and y are integers. x + y < 11 , and x > 6. What is the smallest pos  [#permalink]

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23 Nov 2019, 01:12
The smallest for X is 7. using that in the first equation, we get:

Y<4. The smallest value for Y would be 3. => Smallest value for X-Y would be 7-3 = 4

Ans C
Re: x and y are integers. x + y < 11 , and x > 6. What is the smallest pos   [#permalink] 23 Nov 2019, 01:12
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