|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
15 Oct 2010, 07:27
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:19) correct
33%
(02:16)
wrong
based on 819
sessions
History
Date
Time
Result
Not Attempted Yet
A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the way and this process is continued indefinitely. If a side of the first square is 4 cm. determine the sum of areas of all squares?
A. 18
B. 32
C. 36
D. 64
E. None
A. 18
B. 32
C. 36
D. 64
E. None
15 Oct 2010, 08:21
Kudos
Bookmarks
anilnandyala
Let the side of the first square be \(a\), so its area will be \(area_1=a^2\);
Next square will have the diagonal equal to \(a\), so its area will be \(area_2=\frac{d^2}{2}=\frac{a^2}{2}\);
And so on.
So the areas of the squares will form infinite geometric progression: \(a^2\), \(\frac{a^2}{2}\), \(\frac{a^2}{4}\), \(\frac{a^2}{8}\), \(\frac{a^2}{16}\), ... with common ration equal to \(\frac{1}{2}\).
For geometric progression with common ratio \(|r|<1\), the sum of the progression is \(sum=\frac{b}{1-r}\), where \(b\) is the first term.
So the sum of the areas will be \(sum=\frac{a^2}{1-\frac{1}{2}}=\frac{4^2}{\frac{1}{2}}=32\).
Answer: B.
General Discussion
15 Oct 2010, 08:00
Kudos
Bookmarks
B. 32
form GP s^2 + 2 (s/2)^2 + 4 (s/4)^2
form GP s^2 + 2 (s/2)^2 + 4 (s/4)^2
