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10 Jul 2020, 02:47
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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:
45%
(medium)
Question Stats:
66% (01:34) correct
34%
(01:52)
wrong
based on 213
sessions
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Are x, y, and z consecutive integers?
(1) The remainder when x + y + z is divided by 3 is 2.
(2) The remainder when xyz is divided by 3 is 1.
Are You Up For the Challenge: 700 Level Questions
(1) The remainder when x + y + z is divided by 3 is 2.
(2) The remainder when xyz is divided by 3 is 1.
Are You Up For the Challenge: 700 Level Questions
10 Jul 2020, 03:27
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Bunuel
IMO D.
Sol:
1.every set of consecutive 3 numbers will be a multiple of 3, example-1+2+3=6 so we will not have 2 as a remainder.
Similarly even if one of the number is 0 then we will have 0 +1+2=3 div by 3 give no remainder. so this option tells us that x,y,z are not consecutive.
2. xyz div by 3 gives remainder 1, so again 1*2*3=6, similarly this will always be a multiple of 3 , and in case of zero our case doesn't stand, so we know that x,y,z are not consecutive.
Both options tell us that the x,y and z are not consecutive.
KaramveerBakshi
Joined: 18 Feb 2020
Last visit: 09 Sep 2021
Posts: 288
Given Kudos: 30
Location: India
Schools: HEC Montreal Jindal '23 (S) ISB'22
GMAT 1: 660 Q50 V29
GPA: 3
10 Jul 2020, 03:37
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To find: If x,y, and z are consecutive integers.
Solving:
Statements :
(1) x+y+z, when divided by 3, gives the remainder 2.
A - Observation: For any set of 3 consecutive integers, the sum is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 2; x, y, and z cannot be consecutive integers.
Are x, y, and z consecutive integers? NO.
Sufficient.
(2) Xyz, when divided by 3, give the remainder as 1.
A - Observation: For any set of 3 consecutive integers, the product is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 1; x, y, and z cannot be consecutive integers.
Are x, y, and z consecutive integers? NO.
Sufficient.
Both statements are independently Sufficient.
Therefore, Answer (D)
Solving:
Statements :
(1) x+y+z, when divided by 3, gives the remainder 2.
A - Observation: For any set of 3 consecutive integers, the sum is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 2; x, y, and z cannot be consecutive integers.
Are x, y, and z consecutive integers? NO.
Sufficient.
(2) Xyz, when divided by 3, give the remainder as 1.
A - Observation: For any set of 3 consecutive integers, the product is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 1; x, y, and z cannot be consecutive integers.
Are x, y, and z consecutive integers? NO.
Sufficient.
Both statements are independently Sufficient.
Therefore, Answer (D)
