AS #14

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sat Oct 24, 2015 12:24 pm

14. Is the positive integer X divisible by 21?

(1) When X is divided by 14, the remainder is 4.
(2) When X is divided by 15, the remainder is 5.

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 24, 2015 12:24 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Oct 24, 2015 6:44 pm

For x to be divisible by 21 it has to be divisible by both 3 and 7.

When we have a remainder, r, a number can be expressed as nY + r.

Statement 1 tells us that X = n14 + 4.

In other words X = (n)(2)(7) + 4.

So X = a bunch of 7's + 4. That means X can't be divisible by 7. So X is not divisible by 21 either.

So Statement 1 is sufficient.

Statement 2 tells us that X = n15 + 5.

So X = (n)(5)(3) + 5.

So X = a bunch of 3's + 5. 5 is not divisible by 3. So X is not divisible by 3 or by 21.

So Statement 2 is sufficient.

So the correct answer is D.

Marty Murray
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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Mon Oct 26, 2015 2:04 pm

Marty Murray wrote:For x to be divisible by 21 it has to be divisible by both 3 and 7.

When we have a remainder, r, a number can be expressed as nY + r.

Statement 1 tells us that X = n14 + 4.

In other words X = (n)(2)(7) + 4.

So X = a bunch of 7's + 4. That means X can't be divisible by 7. So X is not divisible by 21 either.

So Statement 1 is sufficient.

Statement 2 tells us that X = n15 + 5.

So X = (n)(5)(3) + 5.

So X = a bunch of 3's + 5. 5 is not divisible by 3. So X is not divisible by 3 or by 21.

So Statement 2 is sufficient.

So the correct answer is D.

So as long as X cannot be divided by 7 OR 3 the question is sufficient?

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Mon Oct 26, 2015 2:15 pm

oquiella wrote:So as long as X cannot be divided by 7 OR 3 the question is sufficient?

21 has two prime factors, 7 and 3. For a number to be divisible by 21 it has to be divisible by both 7 and 3.

So yes, if a statement shows that X is not divisible by 7 or not divisible by 3, then it is sufficient for determining that X is not divisible by 21.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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