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28 Sep 2016, 04:00
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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:
25%
(medium)
Question Stats:
75% (01:37) correct
25%
(01:57)
wrong
based on 566
sessions
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When a positive integer n is divided by 7, what is the remainder?
1) When n-294 is divided by 7, the remainder is 3
2) n-3 is divisible by 7
1) When n-294 is divided by 7, the remainder is 3
2) n-3 is divisible by 7
28 Sep 2016, 13:36
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MathRevolution
Target question: What is the remainder when positive integer n is divided by 7?
Statement 1: When n-294 is divided by 7, the remainder is 3
ASIDE: There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
The statement tells us that when n - 294 is divided by 7, the remainder is 3
So, using the above rule, we can say that: n - 294 = 7k + 3, for some integer k.
Take n - 294 = 7k + 3 and...
...add 294 to both sides to get: n = 7k + 294 + 3 [you'll see why I wrote the right side this way]
Since 294 = (7)(42), we can write: n = 7(k + 42) + 3
This tells us that n is 3 GREATER THAN some multiple of 7.
So, if we divide n by 7, the remainder will be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: n-3 is divisible by 7
In other words, n-3 = 7j for some integer j.
If we add 3 to both sides we get: n = 7j + 3
This tells us that n is 3 GREATER THAN some multiple of 7.
So, if we divide n by 7, the remainder will be 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer =
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28 Sep 2016, 06:52
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MathRevolution
This is how I tried
We have let n be positive integer
n = 7q+x and here x is the reminder.
Stat 1: n-294 = 7q+3
n = 7q+297
now when n is divided by 7 then we get 3 as reminder (297/7 = 3 reminder)...Sufficient.
Stat 2: n-3 = 7q => n = 7q+3.
Now n divided by 7 , we get 3 as reminder...Sufficient.
Option D.
