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# X, Y and Z were the only candidates in a certain election.

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Manager
Joined: 23 Feb 2017
Posts: 58
X, Y and Z were the only candidates in a certain election.  [#permalink]

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12 Jan 2018, 19:40
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15% (low)

Question Stats:

88% (00:59) correct 12% (00:59) wrong based on 33 sessions

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X, Y and Z were the only candidates in a certain election. If Y and Z received votes in the ratio 3 : 4, who won the election?

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Joined: 02 Aug 2009
Posts: 8023
Re: X, Y and Z were the only candidates in a certain election.  [#permalink]

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12 Jan 2018, 20:06
mandeey wrote:
X, Y and Z were the only candidates in a certain election. If Y and Z received votes in the ratio 3 : 4, who won the election?

Hi..

We know from 3:4 that Z>Y..
1) Y<X....
X could be >Z... So ans X
X could be in between Y and Z,. Ans Z
Insuff
2) Z<X..
So X>Z>Y..
Ans X
Sufficient

B
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Re: X, Y and Z were the only candidates in a certain election.  [#permalink]

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12 Jan 2018, 20:12
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mandeey wrote:
X, Y and Z were the only candidates in a certain election. If Y and Z received votes in the ratio 3 : 4, who won the election?

y = 3a and z = 4a. Votes would be integer and positive. So z > y.

1. y < x. No relation between x and z
2. z<x so y<x. So x has most votes.

Ans. B.

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X, Y and Z were the only candidates in a certain election.  [#permalink]

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14 Jan 2018, 22:15
mandeey wrote:
X, Y and Z were the only candidates in a certain election. If Y and Z received votes in the ratio 3 : 4, who won the election?

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

We have 3Z = 4Y from the original condition.

Since we have 3 variables (X, Y and Z) and 1 equations, C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2)
Y < X and Z < X

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
We have Y < X from the condition 1).
However, we don't know if X < Z or X > Z.
The condition 1) only is not sufficient.

Condition 2)
We have X > Z from the condition 2).
Since 3Z = 4Y, we have Z > Y.
Thus we have X > Z > Y and so X won the election.
The condition 2) only is sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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X, Y and Z were the only candidates in a certain election.   [#permalink] 14 Jan 2018, 22:15
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