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## remainder

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 1 member reply
buoyant Master | Next Rank: 500 Posts
Joined
02 Mar 2013
Posted:
106 messages
4

#### remainder

Thu Dec 25, 2014 8:02 pm
If k is an even integer, what is the remainder when k is divided
by 10 ?
(1) The remainder when k is divided by 5 is equal to the
remainder when k is divided by 10.
(2) The remainder is greater than 3.

OA:C

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9662 messages
Followed by:
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GMAT Score:
800
Thu Dec 25, 2014 8:17 pm
Hi buoyant,

This question is perfect for TESTing VALUES, but there are a few Number Properties that are worth noting (and taking advantage of).

We're told that K is an EVEN integer. We're asked for the REMAINDER when K is divided by 10.

Fact 1: K/5 has the same remainder as K/10

Since K has to be EVEN the possible remainders for K/5 are severely limited...

If
K = 12...
12/5 = 2r2
12/10 = 1r2
The answer to the question is 2

K = 14
14/5 = 2r4
14/10 = 1r4
The answer to the question is 4

**Note that K is EVEN, so K/5 means that the remainder MUST be 0, 2 or 4**
Fact 1 is INSUFFICIENT

Fact 2: The remainder is greater than 3

If
K = 14
14/10 = 1r4

K = 16
16/10 = 1r6
Fact 2 is INSUFFICIENT

Combined, we know...
The remainder is either 0, 2 or 4
The remainder is greater than 3
The ONLY value that fits both is 4
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11845 messages
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Fri Dec 26, 2014 12:56 pm
buoyant wrote:
If k is an even integer, what is the remainder when k is divided by 10?

(1) The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
(2) The remainder is greater than 3.

OA:C
Target question: What is the remainder when k is divided by 10?
This question is a good candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Let's make a few observations:
24 divided by 10 equals 2 with remainder 4
70 divided by 10 equals 7 with remainder 0
86 divided by 10 equals 8 with remainder 6
2 divided by 10 equals 0 with remainder 2

As you can see, the remainder (when we divide by 10) will always be the same as the UNITS digit of k. So, we can write....
REPHRASED target question: What is the units digit of k?

Given: k is an EVEN integer
Since k is an EVEN integer, then we know that, the UNITS digit of k will be 0, 2, 4, 6, or 8.

Statement 1: The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
Let's examine all possible cases:
case a: units digit of k is 0: When k is divided by 5, the remainder is 0. When k is divided by 10, the remainder is also 0. So, the units digit of k COULD be 0
case b: units digit of k is 2: When k is divided by 5, the remainder is 2. When k is divided by 10, the remainder is also 2. So, the units digit of k COULD be 2
case c: units digit of k is 4: When k is divided by 5, the remainder is 4. When k is divided by 10, the remainder is also 4. So, the units digit of k COULD be 4
case d: units digit of k is 6: When k is divided by 5, the remainder is 1. When k is divided by 10, the remainder is 6. So, the units digit of k CANNOT be 6
case e: units digit of k is 8: When k is divided by 5, the remainder is 3. When k is divided by 10, the remainder is 8. So, the units digit of k CANNOT be 8
Since the units digit of k COULD be 0, 2 or 4, statement 1 is NOT SUFFICIENT

Statement 2: The remainder [when k is divided by 10] is greater than 3.
In other words, the units digit of k COULD be 4, 6 or 8
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the units digit of k COULD be 0, 2 or 4
Statement 2 tells us that the units digit of k COULD be 4, 6 or 8
The ONLY possible scenario that satisfies BOTH statements is that the units digit of k MUST be 4
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

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Gurpreet singh Senior | Next Rank: 100 Posts
Joined
28 Apr 2016
Posted:
38 messages
1
Sat Jun 18, 2016 10:49 pm
Divisibility rule 0
now k is even so k can be 2, 4, 6 or 8

statement 1 Reminder r is same when k is divided by 5. so reminder could be 2 or 4. -Insufficient
Statement 2 Reminder is greater than 3-could be 2,4,6 or 8.

Combining both the statements reminder is 4

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