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In the trapezoid above, with sides a, b, c, and 1, what is the value o

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In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 30 Apr 2015, 03:17
4
8
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:41) correct 67% (02:00) wrong based on 286 sessions

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In the trapezoid above, with sides a, b, c, and 1, what is the value of ac ?

(1) a + c = b

(2) a – c = 1


Kudos for a correct solution.

Attachment:
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png [ 2.03 KiB | Viewed 3568 times ]

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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 01 May 2015, 12:46
1
ST 1 A+C=B
Draw a line parallel to side-measure 1 from C TO A
Now for the right angle triangle 1^2 + (a-c)^2 = b^2
on solving this we'll get the value of ac ST 1 SUFF
ST 2 A-C=1
Answer = 1
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In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 01 May 2015, 15:17
1
what is the value of ac ?
We have to find a way to create an equation from the trapezoid that will draw an appropriate relationship between the statements and the information given.
Drawing a line parallel to the side that has a value of 1, we create a right triangle with a-c and 1 as its sides and b as its hypotenuse.
Using pythagorean theorem, we obtain the equation (a-c)^2 + 1^2 = b^2
Decomposed, we obtain the equation a^2 - 2ac + c^2 + 1 = b^2

(1) a + c = b
If we square both sides of this entity, it become a^2 + 2ac + c^2 = b^2
we can then use that equation and subtract it from a^2 - 2ac + c^2 + 1 = b^2
ac in this case equals 1/4
Sufficient

(2) a – c = 1
Even after squaring this we are unable to isolate ac into a specific value
Insufficient

Answer: A
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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 04 May 2015, 00:42
Could you please elaborate on Statement 1 and your math??


Ted21 wrote:
ST 1 A+C=B
Draw a line parallel to side-measure 1 from C TO A
Now for the right angle triangle 1^2 + (a-c)^2 = b^2
on solving this we'll get the value of ac ST 1 SUFF
ST 2 A-C=1
Answer = 1
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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 04 May 2015, 16:38
1
kelvind13 wrote:
Could you please elaborate on Statement 1 and your math??


Ted21 wrote:
ST 1 A+C=B
Draw a line parallel to side-measure 1 from C TO A
Now for the right angle triangle 1^2 + (a-c)^2 = b^2
on solving this we'll get the value of ac ST 1 SUFF
ST 2 A-C=1
Answer = 1


Statement 1:
a+c=b
square both sides of the above equation. This then becomes a^2 + 2ac + c^2 = b^2

a^2 + 2ac + c^2 = b^2
-(a^2 - 2ac + c^2 + 1 = b^2)

When we subtract the two equations it becomes

a^2 + 2ac + c^2 = b^2
-a^2 + 2ac - c^2 - 1 = -b^2

which equals
4ac-1=0
4ac=1
ac=(1/4)

Hopefully this helps
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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 02 Aug 2016, 10:38
Bunuel,

Can you please post the complete solution?

Thanks
Akash
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In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 02 Aug 2016, 17:56
1
AkashKashyap wrote:
Bunuel,

Can you please post the complete solution?

Thanks
Akash


Akash

Please refer the fig.attached
(1) a+c=b
sq. both sides
a^2+c^2+2ac=b^2-----------(A)
also from fig the cutout upper right angled triangle having hypotenuse b we can write
(a-c)^2+1^2=b^2
a^2+c^2-2ac+1=b^2-----------(B)
now equate (A) & (B)

a^2+c^2+2ac=a^2+c^2-2ac+1
ac=1/4
suff...

(2) a-c=1
we can only calculate b=sq rt 2 nothing else
insuff...

Ans A
Attachments

lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png [ 4.96 KiB | Viewed 2072 times ]

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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 01 Apr 2017, 08:28
Bunuel wrote:
Image
In the trapezoid above, with sides a, b, c, and 1, what is the value of ac ?

(1) a + c = b

(2) a – c = 1


Kudos for a correct solution.

Attachment:
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png


Great question! thanks for sharing this.
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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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New post 01 Apr 2017, 09:10
1
Bunuel wrote:
Image
In the trapezoid above, with sides a, b, c, and 1, what is the value of ac ?

(1) a + c = b

(2) a – c = 1


Kudos for a correct solution.

Attachment:
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 1 hidden equation from Pythagoras theorem, which is \((a-c)^2 + 1 = b^2\). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. However, this question is not about a single variable, but about ab. We need to look into any relation about \(ab\).

Condition 1)

\((a+c)^2 = b^2 = (a-c)^2 + 1\)
\((a+c)^2 = (a-c)^2 + 1\)
\(a^2 + 2ac + c^2 = a^2 -2ac + c^2 + 1\)
\(2ac = -2ac + 1\)
\(4ac = 1\)
\(ac = 1/4\)

This is sufficient.

Condition 2)

We have \((a-c)^2 + 1 = b^2\).
\(b^2 = 2\)
We can not declare the value of \(ac\).

Thus, this is not sufficient.

Therefore, the correct answer is A.
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Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

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