GRE Prep 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.
A sports apparel company makes basketball shirts in 15 sizes. For each
[#permalink]
12 Sep 2023, 04:00
12 Sep 2023, 04:00
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
66% (02:36) correct
33% (02:36) wrong based on 12 sessions
Hide Show timer Statistics
A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant.
The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
A. \(20 \sqrt{2}\)
B. \(20 \sqrt[14]{2^5}\)
C. \(20 \sqrt[4]{2^7}\)
D. \(20 \sqrt[2]{2^8}\)
E. \(20 \sqrt[2]{2^{14\)
The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
A. \(20 \sqrt{2}\)
B. \(20 \sqrt[14]{2^5}\)
C. \(20 \sqrt[4]{2^7}\)
D. \(20 \sqrt[2]{2^8}\)
E. \(20 \sqrt[2]{2^{14\)
Part of the project: The Butler-GRE Daily New Quant and Verbal Questions to Practice (2023) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: A sports apparel company makes basketball shirts in 15 sizes. For each
[#permalink]
15 Sep 2023, 14:13
15 Sep 2023, 14:13
Hi! I'm not sure how to do this problem. Why are there square roots in the answer choices?
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: A sports apparel company makes basketball shirts in 15 sizes. For each
[#permalink]
15 Sep 2023, 21:58
15 Sep 2023, 21:58
3
A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant. The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
The problem is based on Geometric Progression(GP) with first term (a) as 20 and number of terms (n) as 15.
Size of \(15^{th}\) shirt, \(T_{15}\) = 40.
Let r be the ratio between consecutive sizes.
We need to find the size of \(8^{th}\) shirt, \(T_8\)
Using, GP formula for \(T_n\) we get
\(T_n = a*r^{n-1}\)
=> \(T_{15} = a*r^{15-1}\) = 20 * \(r^{14}\)
=> \(r^{14}\) = \(\frac{40}{20}\) = 2
\(T_8 = a*r^{8-1}\) = 20 * \(r^7\)
We know that \(r^{14}\) = 2
Taking square root on both the sides we will get
\(r^7\) = \(\sqrt{2}\)
=> \(T_8\) = 20 * \(\sqrt{2}\)
So, Answer will be A
Hope it helps!
The problem is based on Geometric Progression(GP) with first term (a) as 20 and number of terms (n) as 15.
Size of \(15^{th}\) shirt, \(T_{15}\) = 40.
Let r be the ratio between consecutive sizes.
We need to find the size of \(8^{th}\) shirt, \(T_8\)
Using, GP formula for \(T_n\) we get
\(T_n = a*r^{n-1}\)
=> \(T_{15} = a*r^{15-1}\) = 20 * \(r^{14}\)
=> \(r^{14}\) = \(\frac{40}{20}\) = 2
\(T_8 = a*r^{8-1}\) = 20 * \(r^7\)
We know that \(r^{14}\) = 2
Taking square root on both the sides we will get
\(r^7\) = \(\sqrt{2}\)
=> \(T_8\) = 20 * \(\sqrt{2}\)
So, Answer will be A
Hope it helps!
