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Difficulty:
55%
(hard)
Question Stats:
61% (01:51) correct
39%
(01:48)
wrong
based on 338
sessions
History
Date
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Result
Not Attempted Yet
Set X consists of ten consecutive integers. Set Y consists of all the distinct integers that result from adding 2 to each of the integers in set X and all the integers that result from subtracting 2 from each of the integers in set X. How many more integers are there in set Y than in set X ?
A. 0
B. 4
C. 10
D. 14
E. 20
A. 0
B. 4
C. 10
D. 14
E. 20
10 Apr 2021, 17:05
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Solution:
SetX: x , x+1, x+2, x+3, x+4, x+5,+x+6 ,x+7, x+8,x+9
Total 10
Set y:
x+2, x+3, x+4, x+5,+x+6 ,x+7, x+8,x+9, x+10, x+11
and
x-2 , x-1, x , x+1,x+2, x+3, x+4, x+5,+x+6 ,x+7
Y becomes: x-2 , x-1, x , x+1,x+2, x+3, x+4, x+5,x+6 ,x+7, x+8,x+9, x+10, x+11
Total 14
Alternatively, say X= 1,2,3,4,5,6,7,8,9,10 = 10 elements
Y becomes =
3,4,5,6,7,8,9,10,11,12
And ,-1,0 , 1,2,3,4,5,6,7,8
-1,0,1,2,3,4,5,6,7,8,9,10,11,12= 14 elements
Hence 4
SetX: x , x+1, x+2, x+3, x+4, x+5,+x+6 ,x+7, x+8,x+9
Total 10
Set y:
x+2, x+3, x+4, x+5,+x+6 ,x+7, x+8,x+9, x+10, x+11
and
x-2 , x-1, x , x+1,x+2, x+3, x+4, x+5,+x+6 ,x+7
Y becomes: x-2 , x-1, x , x+1,x+2, x+3, x+4, x+5,x+6 ,x+7, x+8,x+9, x+10, x+11
Total 14
Alternatively, say X= 1,2,3,4,5,6,7,8,9,10 = 10 elements
Y becomes =
3,4,5,6,7,8,9,10,11,12
And ,-1,0 , 1,2,3,4,5,6,7,8
-1,0,1,2,3,4,5,6,7,8,9,10,11,12= 14 elements
Hence 4
12 Apr 2021, 16:12
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mSKR
Not sure I agree with this - the question stem does not ask for elements in each set, only integers. Further, it specifically states that Y consists of ALL integers that are +, - X values.
Therefore, even if Y has more than one of the same integer, I believe the instruction is such that we count it. Y is therefore higher (I think ~20 integers give or take?)
