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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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30 Apr 2015, 03:17
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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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01 May 2015, 12:46
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ST 1 A+C=B Draw a line parallel to sidemeasure 1 from C TO A Now for the right angle triangle 1^2 + (ac)^2 = b^2 on solving this we'll get the value of ac ST 1 SUFF ST 2 AC=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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01 May 2015, 15:17
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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 ac and 1 as its sides and b as its hypotenuse. Using pythagorean theorem, we obtain the equation (ac)^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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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 sidemeasure 1 from C TO A Now for the right angle triangle 1^2 + (ac)^2 = b^2 on solving this we'll get the value of ac ST 1 SUFF ST 2 AC=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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04 May 2015, 16:38
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kelvind13 wrote: Could you please elaborate on Statement 1 and your math?? Ted21 wrote: ST 1 A+C=B Draw a line parallel to sidemeasure 1 from C TO A Now for the right angle triangle 1^2 + (ac)^2 = b^2 on solving this we'll get the value of ac ST 1 SUFF ST 2 AC=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 4ac1=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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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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02 Aug 2016, 17:56
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 (ac)^2+1^2=b^2 a^2+c^22ac+1=b^2(B) now equate (A) & (B) a^2+c^2+2ac=a^2+c^22ac+1 ac=1/4 suff... (2) ac=1 we can only calculate b=sq rt 2 nothing else insuff... Ans A
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lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqDITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5W_LSClrh9liw7pUognufJTSOvSXIC20UfQ.png [ 4.96 KiB  Viewed 1383 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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01 Apr 2017, 08:28
Bunuel wrote: 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_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqDITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5W_LSClrh9liw7pUognufJTSOvSXIC20UfQ.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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01 Apr 2017, 09:10
Bunuel wrote: 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_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqDITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5W_LSClrh9liw7pUognufJTSOvSXIC20UfQ.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 \((ac)^2 + 1 = b^2\). 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) \((a+c)^2 = b^2 = (ac)^2 + 1\) \((a+c)^2 = (ac)^2 + 1\) \(a^2 + 2ac + c^2 = a^2 2ac + c^2 + 1\) \(2ac = 2ac + 1\) \(4ac = 1\) \(ac = 1/4\) This is sufficient. Condition 2) We have \((ac)^2 + 1 = b^2\). \(b^2 = 2\) 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
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