Problem Solving

BTGmoderatorDC wrote:A post on a website gains a point if a user choose to upvote it and loses a point if a user chooses to downvote it. If a post has a total of 60 points and 40% of the votes were downvotes, how many votes have been cast, in total?

A. 100
B. 150
C. 240
D. 300
E. 500

OA D

Source: Veritas Prep

Say the number of votes cast = x

Thus,

the number of upvotes cast = 60% of x = 0.6x; and
the number of downvotes cast = 40% of x = 0.4x;

total point = 0.6x -0.4x = 0.2x

=> 0.2x = 40

=> x = 300

The correct answer: D

Hope this helps!

-Jay
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Hi All,

We're told that a post on a website gains a point if a user chooses to upvote it and loses a point if a user chooses to downvote it and that a particular post has a total of 60 points (with 40% of the votes being downvotes). We're asked for the total number of votes that have been cast for this post. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first....

Answer B: 150 votes
Since 40% of the votes are downvotes, that means there were (.4)(150) = 60 downvotes
The rest were upvotes, so there were 150 - 60 = 90 upvotes
The total score would be 90 - 60 = 30 points
This is NOT a match for what we were told though (the post is supposed to have a score of 60 points). Thus, we clearly need MORE votes. Notice how 30 is exactly HALF of what we need it to be.... maybe we need to DOUBLE the number of votes...

Answer D: 300 votes
Since 40% of the votes are downvotes, that means there were (.4)(300) = 120 downvotes
The rest were upvotes, so there were 300 - 120 = 180 upvotes
The total score would be 180 - 120 = 60 points
This is an exact match for what we were told, so this must be the answer.

Final Answer: D

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

BTGmoderatorDC wrote:A post on a website gains a point if a user choose to upvote it and loses a point if a user chooses to downvote it. If a post has a total of 60 points and 40% of the votes were downvotes, how many votes have been cast, in total?

A. 100
B. 150
C. 240
D. 300
E. 500

Let u = the number of upvotes and d = the number of downvotes. We can create the equations:

u - d = 60

and

d = 0.4(u + d)

Simplifying the second equation, we have:

d = 0.4u + 0.4d

0.6d = 0.4u

6d = 4u

1.5d = u

Now we can substitute 1.5d for u into the first equation and obtain:

1.5d - d = 60

0.5d = 60

d = 120

Since d = 120, u = 1.5 x 120 = 180. Therefore, a total of 180 + 120 = 300 votes have been cast.

Alternate Solution:

We can test each answer choice:

A) 100 total votes

If 100 votes were cast and 40% were downvotes, then there are 100*(0.4) = 40 downvotes and 100 - 40 = 60 upvotes. In this case, the post would have 60 - 40 = 20 total points. We can eliminate answer choice A.

B) 150 total votes

If 150 votes were cast and 40% were downvotes, then there are 150*(0.4) = 60 downvotes and 150 - 60 = 90 upvotes. In this case, the post would have 90 - 60 = 30 total points. We can eliminate answer choice B.

C) 240 total votes

If 240 votes were cast and 40% were downvotes, then there are 240*(0.4) = 96 downvotes and 240 - 96 = 144 upvotes. In this case, the post would have 144 - 96 = 48 total points. We can eliminate answer choice C.

D) 300 total votes

If 300 votes were cast and 40% were downvotes, then there are 300*(0.4) = 120 downvotes and 300 - 120 = 180 upvotes. In this case, the post would have 180 - 120 = 60 total points, as required. The answer is D.

Answer: D