Problem Solving

In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

The OA is C .

How can I get the answer here? Experts, may you help me here. Please.

VJesus12 wrote:In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

The OA is C .

How can I get the answer here? Experts, may you help me here. Please.

Candidate Z received 24,000 votes.

If candidate Y received 1/4 fewer votes than Z, we know Y received (1/4)*24,000 = 6000 fewer votes, or 24,000 - 6000 = 18,000 votes.

If X received 1/3 more votes than Y, then X received (1/3)* 18,000 = 6000 more votes than Y, or 18,000 + 6000 = 24,000 vote. The answer is C

VJesus12 wrote:In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

The OA is C .

How can I get the answer here? Experts, may you help me here. Please.

Fun little shortcut: Reducing a value by 1/4 is the equivalent of multiplying it by1 - 1/4, or 3/4.
Increasing a value by 1/3 is the equivalent of multiplying it by 1 + 1/3, or 4/3.
If we multiply some value by 3/4 * 4/3, then we're going to end up right back where we started.

In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

The OA is C .

How can I get the answer here? Experts, may you help me here. Please.

Hi VJesus12,
Let's take a look at your question.

Votes candidate Z received = 24,000
Candidate Y received 1/4 fewer votes than Candidate Z.

Let's first find 1/4 of Candidate Z votes.
$$=\frac{1}{4}\times24,000=6000$$

Number of votes Candidate Y received
$$=24,000-6000=18,000$$

The questions states that Candidate X received 1/3 more votes than Candidate Y.
1/3 of candidate Y's votes
$$=\frac{1}{3}\times18,000=6000$$

Number of votes Candidate X received
$$=18,000\ +6,000=24,000$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.