Problem Solving

the_silver_lining wrote:Hi, I know this has been posted before. but i have not understood a concept. Please some one explain.

If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?
A. 12
B. 13
C. 14
D. 15
E. 16

let Mike=M
therefore, kelley = M+(1/3)m = (4/3)M
total votes = M + (4/3)M = (7/3)M
I understood till the step where Total votes = (7/3)M.But, why should we take M as a multiple of 7?? Wont the total number of votes become a fraction if we
chose an answer choice with a multiple of 7. which is 14.

I like your approach, but I'll put a slight twist on it.
Let M = Mike's votes
Therefore, (4/3)M = Kelly's votes
So, the ratio of Mike's votes to Kelly's votes = M : (4/3)M

IMPORTANT: Let's eliminate the fraction by multiplying both parts of the ratio by 3. This gives us an equivalent Mike to Kelly ratio of 3M : 4M

From here, if we add both parts we get 3M + 4M = 7M

This tells us that the Mike's votes and Kelly's votes must be a multiple of 7.

Answer = C

Cheers,
Brent

the_silver_lining wrote: let Mike=M
therefore, kelley = M+(1/3)m = (4/3)M
total votes = M + (4/3)M = (7/3)M
I understood till the step where Total votes = (7/3)M.But, why should we take M as a multiple of 7?? Wont the total number of votes become a fraction if we
chose an answer choice with a multiple of 7. which is 14.

Here's another response to your question.

In your solution, you correctly conclude that the total number of votes = (7/3)M
Since the total number of votes must be an integer, we can see that M must be divisible by 3. Otherwise (7/3)M will not be an integer.

Also notice that we can rewrite (7/3)M as (7)(1/3)M. This tells us that (7/3)M must be a multiple of 7.

Cheers,
Brent

Hi maanda82,

Your algebraic approach is certainly correct. Since much of what you'll be tested on in the Quant section is more about patterns than what you might find on a typical math test, sometimes you can avoid the longer "math" approaches and quickly spot a pattern just by "playing around" with the information in the prompt.

Here, we're told that Kelly received 1/3 MORE votes than Mike....

If Mike got 3 votes, then Kelly got 4 --> 7 total
If Mike got 6 votes, then Kelly got 8 --> 14 total
If Mike got 9 votes, then Kelly got 12 --> 21 total
Etc.

The total MUST be a multiple of 7. From here, it's not hard to check the answers and find the multiple of 7. Layered algebra steps are not required to figure out this pattern.

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

the_silver_lining wrote:
If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?
A. 12
B. 13
C. 14
D. 15
E. 16

If we let k = the number of votes Mike received, then (4/3)k = the number of votes Kelly received. Thus, they received a total of k + 4k/3 = 3k/3 + 4k/3 = 7k/3 votes.

Since 7k/3 has to be an integer, k can be any multiple of 3.

When k is 3, the total number of votes is 7(3)/3 = 7.

When k is 6, the total number of votes is 7(6)/3 = 14.

Answer: C