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# What is the value of x ? (1) xy = 6 (2) x + y = 5

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
What is the value of x ? (1) xy = 6 (2) x + y = 5  [#permalink]

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15 Jan 2018, 08:38
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Difficulty:

15% (low)

Question Stats:

77% (01:00) correct 23% (00:49) wrong based on 65 sessions

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What is the value of x ?

(1) xy = 6
(2) x + y = 5

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Joined: 07 Dec 2017
Posts: 1153
Re: What is the value of x ? (1) xy = 6 (2) x + y = 5  [#permalink]

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15 Jan 2018, 08:50
Bunuel wrote:
What is the value of x ?

(1) xy = 6
(2) x + y = 5

As our expressions are small, we'll try simple numbers to show us the answer.
This is an Alternative approach.

(1) x=1,y=6 solve the equation as do x=2,y=3.
Insufficient!

(2) x=1,y=4 solve the equation as do x=2,y=3.
Insufficient!

Combined: x=2,y=3 solve the equation as do x=3,y=2.
Still insufficient!

(E) is our answer.
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Re: What is the value of x ? (1) xy = 6 (2) x + y = 5  [#permalink]

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15 Jan 2018, 12:29
Bunuel wrote:
What is the value of x ?

(1) xy = 6
(2) x + y = 5

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.

Since we have 2 variables and 0 equations, C is most likely to be the answer. So, we should consider 1) & 2) first, since we can save time by first checking whether conditions 1) and 2) are sufficient, when taken together.

Conditions 1) & 2)
We have two solutions $$x = 2, y = 3$$ or $$x = 3, y = 2$$.
Since we don't have a unique solution, both conditions together are not 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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Re: What is the value of x ? (1) xy = 6 (2) x + y = 5  [#permalink]

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16 Jan 2018, 00:37
Bunuel wrote:
What is the value of x ?

(1) xy = 6
(2) x + y = 5

Since we are not given anything about y, so individually none of the two statements are sufficient to answer the question. Lets combine the two statements and try.

From second statement, y = 5-x. Substituting this value of y in first statement:
x(5-x) = 6
5x - x^2 = 6
x^2 - 5x + 6 = 0 Or (x-2)(x-3) = 0.
So x could be either 2 or 3. A single unique value of x cannot be determined. Thus Insufficient.

Hence E answer
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Re: What is the value of x ? (1) xy = 6 (2) x + y = 5  [#permalink]

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16 Jan 2018, 05:39
Bunuel wrote:
What is the value of x ?

(1) xy = 6
(2) x + y = 5

Note that both statements are symmetrical in x and y. So even though you will get a pair of values that satisfy them, you will not know which is x and which is y.
Hence answer will be (E)

P.S. The statements should make you think of solving a quadratic equation.
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Re: What is the value of x ? (1) xy = 6 (2) x + y = 5   [#permalink] 16 Jan 2018, 05:39
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