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PriyankaPalit7
Joined: 28 May 2018
Last visit: 13 Jan 2020
Posts: 117
Given Kudos: 883
Location: India
Schools: ISB '21 (A)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
23 Apr 2019, 00:21
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D
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Difficulty:
95%
(hard)
Question Stats:
34% (02:25) correct
66%
(02:54)
wrong
based on 136
sessions
History
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If \(k\) and \(m\) are positive integers, what is the remainder when \(k\) is divided by \(m +1\)?
(1) \(k-m\) when divided by \(m+1\) leaves a remainder \(1\)
(2) \(\frac{k}{3}\) and \(\frac{k}{2}\) when divided by \(m+1\) leave a remainder equal to \(4\) and \(3\) respectively.
(1) \(k-m\) when divided by \(m+1\) leaves a remainder \(1\)
(2) \(\frac{k}{3}\) and \(\frac{k}{2}\) when divided by \(m+1\) leave a remainder equal to \(4\) and \(3\) respectively.
25 Apr 2019, 00:46
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If \(k\) and \(m\) are positive integers, what is the remainder when \(k\) is divided by \(m +1\)?
(1) \(k-m\) when divided by \(m+1\) leaves a remainder \(1\)
This means the remainders when k and m are divided by m+1 add upto 1
When m is divided by m+1, the remainder is m, and let the remainder be R when k is divided by m+1..
so R-m=1, or R=m+1.
Thus, remainder when k is divided by m+1 is m+1 or 0.
Sufficient.
(2) \(\frac{k}{3}\) and \(\frac{k}{2}\) when divided by \(m+1\) leave a remainder equal to \(4\) and \(3\) respectively.
So, \(\frac{k}{3}=(m+1)a+4......k=3(m+1)a+12\) and \(\frac{k}{2}=(m+1)b+3......k=2(m+1)b+6\)..
Thus, 3(m+1)a+12=2(m+1)b+6......(3a-2b)(m+1)=6...
Thus, m+1 will be a factor of 6.
Now, k=3(m+1)a+12 tells us that k is a multiple of 3, and k=2(m+1)b+6 tells us that k is a multiple of 2, OR k is a multiple of both 2 and 3, that is multiple of 6.
Thus, k is a multiple of 6, while m+1 is a factor of 6. So k is a multiple of m+1.
Suff
D
Now, k is a mult
(1) \(k-m\) when divided by \(m+1\) leaves a remainder \(1\)
This means the remainders when k and m are divided by m+1 add upto 1
When m is divided by m+1, the remainder is m, and let the remainder be R when k is divided by m+1..
so R-m=1, or R=m+1.
Thus, remainder when k is divided by m+1 is m+1 or 0.
Sufficient.
(2) \(\frac{k}{3}\) and \(\frac{k}{2}\) when divided by \(m+1\) leave a remainder equal to \(4\) and \(3\) respectively.
So, \(\frac{k}{3}=(m+1)a+4......k=3(m+1)a+12\) and \(\frac{k}{2}=(m+1)b+3......k=2(m+1)b+6\)..
Thus, 3(m+1)a+12=2(m+1)b+6......(3a-2b)(m+1)=6...
Thus, m+1 will be a factor of 6.
Now, k=3(m+1)a+12 tells us that k is a multiple of 3, and k=2(m+1)b+6 tells us that k is a multiple of 2, OR k is a multiple of both 2 and 3, that is multiple of 6.
Thus, k is a multiple of 6, while m+1 is a factor of 6. So k is a multiple of m+1.
Suff
D
Now, k is a mult
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