Events & Promotions
|
|
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.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
29 Jun 2021, 04:45
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
58% (02:44) correct
42%
(02:42)
wrong
based on 210
sessions
History
Date
Time
Result
Not Attempted Yet
Three numbers are in geometric progression such that the product of them is 27 and the sum of the products taken in pairs is 91. What is the third number in the progression?
(A) 1/3
(B) 3
(C) 9
(D) 27
(E) 1/3 or 27
(A) 1/3
(B) 3
(C) 9
(D) 27
(E) 1/3 or 27
29 Jun 2021, 05:14
Kudos
Bookmarks
You don't need to know what a "geometric progression" is on the GMAT, but it's a sequence where we multiply by some constant to find the next term. So here, if a is the first term, and we multiply by r to find each subsequent term, we could write the three terms this way:
a, ar, ar^2
But if that's a geometric sequence, so is this:
ar^2, ar, a
because here we're multiplying by 1/r to find the next term. These sequences have exactly the same terms, so will have the same product, and the same "sum of products taken in pairs". So there will need to be two different solutions here unless every term of the sequence is identical, and since we can quickly confirm that's not the case (the terms would need to all be 3 since their product is 27, but then we don't get the right "sum of terms taken in pairs"). So the answer must be E.
Or you can use the notation above and the fact that the product is 27 to see that (a)(ar)(ar^2) = 27, so a^3 * r^3 = 27, and ar = 3. Since ar is the second term, we know the middle term of the sequence is 3. Then it's easy enough to test answer choices. There's also an algebraic way to deal with the "sum of products taken in pairs" -- you can rewrite the equation ar = 3 as: a = 3/r. Then substituting for "a", the terms of the sequence become 3/r, 3, 3r, and then we can use the fact that the "sum of products taken in pairs is 91" to produce an equation. That equation, though, is a messy quadratic (one solution is not an integer), one that doesn't have any immediately obvious factorization, so algebra is not a very fun way to complete the question.
a, ar, ar^2
But if that's a geometric sequence, so is this:
ar^2, ar, a
because here we're multiplying by 1/r to find the next term. These sequences have exactly the same terms, so will have the same product, and the same "sum of products taken in pairs". So there will need to be two different solutions here unless every term of the sequence is identical, and since we can quickly confirm that's not the case (the terms would need to all be 3 since their product is 27, but then we don't get the right "sum of terms taken in pairs"). So the answer must be E.
Or you can use the notation above and the fact that the product is 27 to see that (a)(ar)(ar^2) = 27, so a^3 * r^3 = 27, and ar = 3. Since ar is the second term, we know the middle term of the sequence is 3. Then it's easy enough to test answer choices. There's also an algebraic way to deal with the "sum of products taken in pairs" -- you can rewrite the equation ar = 3 as: a = 3/r. Then substituting for "a", the terms of the sequence become 3/r, 3, 3r, and then we can use the fact that the "sum of products taken in pairs is 91" to produce an equation. That equation, though, is a messy quadratic (one solution is not an integer), one that doesn't have any immediately obvious factorization, so algebra is not a very fun way to complete the question.
29 Jun 2021, 05:41
Kudos
Bookmarks
Let three numbers be \(\frac{a}{r},\) a, a*r
\(a^3\) = 27
a = 3
Also, sum of \(a^2/r, a^2, and a^2*r \)is 91
so, \(a^2{[1/r+1+r]} = 91\)
\({1/r+1+r} = 91/9 = (90 + 1)/9 = 10 + 1/9 \)
\(1/r + r = 10-1 + 1/9 = 9+1/9\)
r = 9 or 1/9
third number i.e ar can be either \(3*9=27\) or \(3*1/9= 1/3\)
E is the right answer
\(a^3\) = 27
a = 3
Also, sum of \(a^2/r, a^2, and a^2*r \)is 91
so, \(a^2{[1/r+1+r]} = 91\)
\({1/r+1+r} = 91/9 = (90 + 1)/9 = 10 + 1/9 \)
\(1/r + r = 10-1 + 1/9 = 9+1/9\)
r = 9 or 1/9
third number i.e ar can be either \(3*9=27\) or \(3*1/9= 1/3\)
E is the right answer
Bunuel
