GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Sep 2018, 16:33

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49206
In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 30 Apr 2015, 04:17
4
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:37) correct 67% (02:04) wrong based on 265 sessions

HideShow timer Statistics

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
lnzFUe1NsWpRHYetrW_BAMHT3M0ml9ssJU6sexynIY0SxO2MrXLRX71d4EjIqD-ITXHoVyRCXvhKECDrtvrdwtt0Q9b1h5-W_LSClrh9liw7pUognufJTS-OvSXIC20UfQ.png [ 2.03 KiB | Viewed 3146 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 01 Jan 2015
Posts: 56
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 01 May 2015, 13:46
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
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Reviews Badge
In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 01 May 2015, 16:17
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
Intern
Intern
avatar
Joined: 06 Apr 2015
Posts: 35
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 04 May 2015, 01:42
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
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 04 May 2015, 17:38
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
Intern
Intern
avatar
Joined: 13 Sep 2014
Posts: 24
Concentration: Entrepreneurship, Strategy
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 02 Aug 2016, 11:38
Bunuel,

Can you please post the complete solution?

Thanks
Akash
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 984
In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 02 Aug 2016, 18:56
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 1668 times ]

Manager
Manager
avatar
G
Joined: 28 Jul 2016
Posts: 135
Premium Member
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 01 Apr 2017, 09:28
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.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6204
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o  [#permalink]

Show Tags

New post 01 Apr 2017, 10:10
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: In the trapezoid above, with sides a, b, c, and 1, what is the value o &nbs [#permalink] 01 Apr 2017, 10:10
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.