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

Question

https://gmatclub.com/forum/download/file.php?id=26485 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 lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png

Vaibhav21 · Answer

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

peachfuzz · Answer

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

kelvind13 · Answer

Could you please elaborate on Statement 1 and your math??

peachfuzz · Answer

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

AkashKashyap · Answer

Bunuel,

Can you please post the complete solution?

Thanks
Akash

rohit8865 · Answer

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

MathRevolution · Answer

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.

KarishmaB · Answer

Refer to the figure given by rohit8865 above: https://gmatclub.com/forum/in-the-trape ... l#p1718294 That is how we can link b with a and c. So we know that b^2 = 1 + (a-c)^2 (By Pythagorean theorem) (1) a + c = b (a+c)^2 = 1 + (a-c)^2 ac = 1/4 Sufficient alone (2) a – c = 1 Then, b = sqrt(2) but we do not know anything about a and c. We know that the diff between them is 1 so if a = 4, b = 3 and if a = 6, b = 5 etc but we don't know what a and c are. Imagine that we hold the trapezoid from the top and can stretch it up as much as we wish. The values of a and c will keep changing but all else will stay the same. Hence we cannot get the value of ac. Not sufficient. Answer (A)

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

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GMAT Data Sufficiency (DS) Questions

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

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