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If 52x + 604 = 1400 and 151 + 13y

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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
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GMATPrepNow wrote:
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

To avoid unnecessary calculations if we can find a relationship between two equations then it will make our life easy.
Seeing 52x + 604 = 1400 and 151 + 13y = 350, immediately it pops out that 52 is a multiple of 13. 13*4=52.
Now, we multiple equation two with 4 we will get eventually get the same values as equation 1 in terms of y. 604 + 52y = 1400.
So, x-y=0.

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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
1
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GMATPrepNow wrote:
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

This can be solved in many ways. But the easiest of all - is to find relation between two equation.
This will take less time to solve this problem and will enable us to solve difficult question with more time in hand.

Let's take 2nd equation: 151 + 13y = 350. The only hint we have here is 13*4 = 52.
So lets multiply this equation by 4 ==> 604 + 52y = 1400.

The first equation is 52x + 604 = 1400.

==> x and y have same value. Hence x-y = 0.
Ans - C
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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
1
Kudos
GMATPrepNow wrote:
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

If we divide 52x + 604 = 1400 by 4, it becomes 13x + 151 = 350. It means x = y

So x - y = 0

C.
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If 52x + 604 = 1400 and 151 + 13y [#permalink]
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Kudos
Top Contributor
GMATPrepNow wrote:
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

The key here is to avoid solving the two equations for x and y.

As others have show, we can do this by recognizing that each term in the equation 52x + 604 = 1400 is 4 times each term in the equation 151 + 13y = 350
For example, (4)(151) = 604
And (4)(13) = 52
And (4)(350) = 1400

So, if we take 151 + 13y = 350 and multiply both sides by 4, we get the EQUIVALENT EQUATION: 604 + 52y = 1400
Rearrange to get: 52y + 604 = 1400

So, we have:
52x + 604 = 1400
52y + 604 = 1400

Since both equations are set equal to 1400, we can say: 52x + 604 = 52y + 604
Subtract 604 from both sides to get: 52x = 52y
Divide both sides by 52 to get: x = y
If x = y, then x - y = 0

Cheers,
Brent
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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
BrentGMATPrepNow wrote:
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

$$52x = 796$$

Or, $$x = 15.$$xxxx

$$13y = 199$$

Or, $$y = 15.$$xxxx

Hence, $$x – y = 15 - 15 = 0$$, Answer must be (C)
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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x – y?

A) -11/13
B) -11/52
C) 0 --> correct: 52x + 604 = 1400 => 13x +151=350 =>13x=350-151 --(i) & 151 + 13y = 350 => 13y=350-151--(ii) => so (i)-(ii) =>13x-13y=0 => x-y=0
D) 11/52
E) 11/13
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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
It’s simple
1400= 604+52(15.30) > How 15.30 > 1400-604=796 >796/52 > x=15.30
Same for
350 = 151+13(15.30) > 350-151 = 191/13=15.30 >y=15.30
X-Y =15.30-15.30 =0

Posted from my mobile device
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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
52x + 604 = 1400 and 151 + 13y = 350

=> Divide the equation by '4' we get => 13x + 151 = 350

=> 13x - 13 y = 0

=> x - y = 0

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Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
Take Eqn 52x + 604 = 1400
Divide both sides by 4
=> 13x +151 = 350
=>13x=199------1

Take Eqn 151 + 13y = 350
=> 13y=350-151 = 199------2

Subtracting 1 & 2

=>13x-13y=0
=>x-y=0

Hence C
Re: If 52x + 604 = 1400 and 151 + 13y [#permalink]
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