GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 16:59 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

11 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:25) correct 28% (01:45) wrong based on 176 sessions

HideShow timer Statistics

If a, b, and c are positive integers and $$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$, is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Senior Manager  B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

2
ziyuen wrote:
If a, b, and c are positive integers and $$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$, is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

Hi

Multiplying both sides by 30:

5a + 6b = c

(1) b is divisible by 5.

b=5x

5a + 6*5x = c

5(a + 6x) = c ----> c is a multiple of 5. Sufficient.

(2) a is even

a = 2y

10y + 6b = c

c is even, but depending on y and b it may o may not be multiple of 5. Insufficient.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

Top Contributor
2
ziyuen wrote:
If a, b, and c are positive integers and $$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$, is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

Target question: Is c divisible by 5?

Given: a/6 + b/5 = c/30
First let's eliminate the fractions by multiplying both sides of the equation be the least common multiple of 6, 5 and 30.
So, we'll multiply both sides by 30 to get: 5a + 6b = c

Statement 1: b is divisible by 5
We can apply a useful divisibility rule that says: "If j is divisible by x and k is divisible by x, then (j+k) is divisible by x"
We can ready see that 5a is divisible by 5.
And, if b is divisible by 5, then we know that 6b is divisible by 5.
So, by the above rule, we know that 5a + 6b is divisible by 5.
Since 5a + 6b = c, we can conclude that c IS divisible by 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a is even
There are several cases that satisfy statement 2. Here are two:
Case a: a = 2 and b = 5. we know that c = 5a + 6b. So, c = 5(2) + 6(5) = 40, which is divisible by 5. In this case, c IS divisible by 5
Case b: a = 2 and b = 1. we know that c = 5a + 6b. So, c = 5(2) + 6(1) = 16, which is NOT divisible by 5. In this case, c is NOT divisible by 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEO

_________________
Director  S
Joined: 12 Nov 2016
Posts: 699
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

hazelnut wrote:
If a, b, and c are positive integers and $$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$, is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

We don't really mind the equation here we just have to focus on

5a + 6b =30

Basically- the only thing you need to know in this question is whether 6 is a multiple of 5- if 6 is a multiple of 5 then C must be divisible by five because the sum of the two numbers that share a common multiple will always be divisible by that common multiple

Statement 1 is all you need

A
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15294
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

Hi All,

This DS question can be solved in a number of different ways. It's perfect for TESTing Values, but there's also a Number Property built into it that you might find useful. To start, "rewriting" the given equation is a must:

5A + 6B = C

We're also told that A, B and C are positive integers. We're asked if C is a multiple of 5? This is a YES/NO question.

1) B is a MULTIPLE of 5.

You can absolutely TEST Values here, but here's the Number Property worth knowing…

Since A is an integer, 5A is a MULTIPLE of 5
We're told that B is a multiple of 5, so 6B is also MULTIPLE of 5

If you add a multiple of 5 to another multiple of 5, then you will end up with a MULTIPLE of 5.
So, C will ALWAYS be a multiple of 5
Fact 1 is SUFFICIENT

2) A is even

5A will be multiple of 5, since 5(even) is a multiple of 5
However, 6B may or may not be a multiple of 5, depending on what B is.
For example, if B=1, then 6B = 6; if B = 5, then 6B = 30

There's no way to know if we'll end up with a sum that is a multiple of 5 or not.
Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2345
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

hazelnut wrote:
If a, b, and c are positive integers and $$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$, is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

Analyzing the question stem:

$$\frac{a}{6} + \frac{b}{5} = \frac{c}{30}$$........Multiply by 30

$$5a + 6b = c$$

C is multiple of 5, if both terms are multiple of 5....... We see that (5a) is multiple of 5, so (6b) must be multiple of b to make c divisible by 5

The question could rephrased:

Is B multiple of 5??

(1) b is divisible by 5.

This directly answers the question.

Sufficient

(2) a is even.

It does not affect b so it does not help answer the question

Insufficient

Non-Human User Joined: 09 Sep 2013
Posts: 13317
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl   [#permalink] 01 Oct 2019, 01:15
Display posts from previous: Sort by

If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  