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05 Jul 2020, 10:47
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:42) correct
42%
(01:15)
wrong
based on 187
sessions
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Three distinct positive integers sum to 10. Is one of the three integers equal to 5?
(1) One of the three integers is equal to 4.
(2) All three of the integers are less than 6.
(1) One of the three integers is equal to 4.
(2) All three of the integers are less than 6.
05 Jul 2020, 11:28
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From statement 1
If one of the integer is 4 then sum of other two integers is 6 which can only be 1 and 5 because all three are distinct integers.
Sufficient
From statement 2
Only 2,3 and 5 and 1,4 and 5 are the possibilities
Sufficient
Answer choice is D
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If one of the integer is 4 then sum of other two integers is 6 which can only be 1 and 5 because all three are distinct integers.
Sufficient
From statement 2
Only 2,3 and 5 and 1,4 and 5 are the possibilities
Sufficient
Answer choice is D
Posted from my mobile device
05 Jul 2020, 11:43
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abrutlag
Given: Three distinct positive integers sum to 10.
Asked: Is one of the three integers equal to 5?
(1) One of the three integers is equal to 4.
Let the other 2 distinct positive integer be x & y.
4 + x + y = 10
x + y = 6
(x,y) = {(1,5),(5,1)}; One of the 3 distinct positive integers is 5.
(x,y) = {(2,4),(4,2),(3,3)} are not possible since they are distinct positive integers
SUFFICIENT
(2) All three of the integers are less than 6.
Let the 3 distinct positive integer be x, y & z.
Without loss of generalities, we can assume
0<x<y<z<6
x + y + z = 10
(x,y,z) = {(2,3,5),(1,4,5)}
One of the integers must be 5.
SUFFICIENT
IMO D
