Candidates A, B, and C competed in an election. This election usually

Question

Candidates A, B, and C competed in an election. This election usually comprises two rounds. In the first round, all three candidates compete. A candidate qualifies for the second round only if he/she receives at least 20% of the votes cast in the first round. If two candidates receive less than 20% of the votes cast, the other candidate wins the election by default. If a candidate receives more than 60% of the votes in the first round, he/she wins the election without the second round. Was there a second round of election?

(1) The votes received by Candidates A and B together is 82% of the total votes cast.

(2) The votes received by Candidates C and B together is 42% of the total votes cast.

(1) The votes received by Candidates A and B together is 82% of the total votes cast.

(2) The votes received by Candidates C and B together is 42% of the total votes cast.

chetan2u · Accepted Answer

(1) The votes received by Candidates A and B together is 82% of the total votes cast.
So, C gets 18% of votes.
If any of A and B gets less than 20% votes, then the other wins directly. 
But, both A and B can also get more than 20% votes, leading to second round => A = 42%, B=40% and C=18%....Second round
A=61%, B=21% and C=18%....No second round
Insufficient

(2) The votes received by Candidates C and B together is 42% of the total votes cast.
So, A receives 100-42 or 58%.
B+C = 42%, so at least one of them gets more than 20% votes.
Thus, none of the candidate gets >60% and at least two of them get more than 20%. Hence there will certainly be a second round.
Sufficient

B

MartyMurray · Answer

Candidates A, B, and C competed in an election. This election usually comprises two rounds. In the first round, all three candidates compete. A candidate qualifies for the second round only if he/she receives at least 20% of the votes cast in the first round. If two candidates receive less than 20% of the votes cast, the other candidate wins the election by default. If a candidate receives more than 60% of the votes in the first round, he/she wins the election without the second round. Was there a second round of election?

(1) The votes received by Candidates A and B together is 82% of the total votes cast.

(2) The votes received by Candidates C and B together is 42% of the total votes cast.

All the information in the passage boils down to one thing: If one candidate wins over 60% of the votes in the first round, there will be no second round. Otherwise, there will be a second round.

After all, if two candidates receive less than 20% each, then the third candidate receives over 60%.

So, with regard to how many rounds there will be, the information presented all means the same thing.

(1) The votes received by Candidates A and B together is 82% of the total votes cast.

This information indicates that C received under 20% of the votes since 100% - 82% = 18%.

At the same time, it does not indicate whether A or B did or did not win over 60% of the votes.

Insufficient.

(2) The votes received by Candidates C and B together is 42% of the total votes cast.

Since 42% < 60% and 100% - 42% < 60%, this information indicates that no candidate won over 60% of the votes.

So, it confirms that there will be a second round.

Sufficient.

Correct answer:   B

minionbaba · Answer

Hi  Bunuel , this question is also available in OG 2025-26. You can add that tag too. Thank you!

Bunuel · Answer

Added the tag. Thank you!

wickedvikram · Answer

My only concern with this question is that it never explicitly states that these 3 are the only candidates competing. Do we assume them being only competing parties in such questions unless stated otherwise?

MartyMurray · Answer

Generalizing in that way is dangerous because Data Sufficiency questions can play on assumptions like that one.

What we can do instead is look for clues in the prompt.

In this case, the wording of the prompt indicates multiple times that the three candidates are the only ones competing.

In the first round, all three candidates compete.  - This suggests that the three candidates are "all" the candidates.

If two candidates receive less than 20% of the votes cast, the other candidate wins the election by default.  - This indicates that there are only "two" and the "other," meaning that there are three candidates in total.

If a candidate receives more than 60% of the votes in the first round, he/she wins the election without the second round.  - This idea logically matches what the previous sentence says about two candidates receiving less than 20% each, since 100% - 20% - 20% = 60%, helping to confirm that there are only three candidates.

Given the above, we can safely presume that the point is that there are three candidates in total.

egmat · Answer

Hi wickedvikram,

Good instinct to check the setup, because both solutions in the thread lean on it. Notice the step where chetan2u and Marty wrote "A =  100  -  42  =  58% " for Statement ( 2 ), and "C =  100  -  82  =  18% " for Statement ( 1 ). That subtraction only works if A, B, and C's votes together make up the  whole  100% .

Here's why you're safe to assume exactly three candidates.  Read the opening line literally:  "Candidates A, B, and C competed in an election... In the first round, all three candidates compete."  The question is naming the full field, not giving you a sample of it. On the GMAT, when a prompt lists the participants like this - especially with the phrase  "all three candidates"  - that  is  the complete set. There's no hidden fourth candidate to account for.

This is a general convention:  take the stimulus at face value.  The test never expects you to invent unstated players, extra people, or missing options. If a fourth candidate mattered, the question would have to mention them - otherwise the percentages could never be pinned down and the problem would be unsolvable.

Quick check on why it has to be this way:  suppose you  did  allow an unnamed Candidate D. Then Statement ( 2 )'s "B + C =  42% " would tell you nothing about A, because A + D would share the other  58%  in unknown proportions. The clean deduction "A =  58% " collapses, and the statement stops being  sufficient . The only reading that makes the question work - and the reading the wording points to - is that A, B, and C account for all the votes.

So yes: treat them as the only candidates, let their shares sum to  100% , and Statement ( 2 ) gives you A =  58% , forcing a second round.

Answer: B

Candidates A, B, and C competed in an election. This election usually

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GMAT Data Sufficiency (DS) Questions

Candidates A, B, and C competed in an election. This election usually

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