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

It is currently 13 Nov 2019, 00:31

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 a certain supermarket, a triangular display of cans is arranged in

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58993
In a certain supermarket, a triangular display of cans is arranged in  [#permalink]

Show Tags

New post 16 Oct 2019, 00:14
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:03) correct 34% (02:41) wrong based on 29 sessions

HideShow timer Statistics

In a certain supermarket, a triangular display of cans is arranged in 8 rows, numbered 1 through 8 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 95 cans in the entire display, how many cans are in the fifth row?

A. 10
B. 11
C. 13
D. 14
E. 16

_________________
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1049
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: In a certain supermarket, a triangular display of cans is arranged in  [#permalink]

Show Tags

New post 16 Oct 2019, 00:22
Bunuel wrote:
In a certain supermarket, a triangular display of cans is arranged in 8 rows, numbered 1 through 8 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 95 cans in the entire display, how many cans are in the fifth row?

A. 10
B. 11
C. 13
D. 14
E. 16


Let the number of cans in the first row = x
Each row below has 3 more than the row above it
--> Total number of cans in 8 rows = x + (x+3) + (x+6) + . . . . . . (x+21) = 8x + 84

Total is less than 95
--> 8x + 84 < 95
--> 8x < 11
--> Only possible value of x = 1

--> Number of cans in 5th row = x + 12 = 1 + 12 = 13

IMO Option C
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3134
Re: In a certain supermarket, a triangular display of cans is arranged in  [#permalink]

Show Tags

New post 20 Oct 2019, 12:36

Solution



Given
    • In a certain supermarket, a triangular display of cans is arranged.
    • The display has 8 rows, numbered 1 through 8 from top to bottom.
    • Each successively numbered row contains 3 more cans than the row immediately above it.

To find
    • The number of cans in the fifth row if there are fewer than 95 cans in the entire display.

Approach and Working out

Let row 1 has ‘a’ cans.
    • Hence, row 2 has ‘a + 3’ cans.
    • Row 3 = ‘a + 6’ cans
    • Similarly, each successive row has 3 more cans.
      o Hence, cans are in an arithmetic progression with:
      o a = being the number of cans in the first row and,
      o 3= being the common difference,
      o 8 = number of rows

    • Therefore, total cans =\(\frac{8}{2}\)(2a + (8-1)3) = 4(2a + 21)
      o 4(2a + 21) < 95
      o 2a + 21 < \(\frac{95}{4}\)
      o 2a < \(\frac{95}{4}\) – 21
      o 2a < \(\frac{11}{4}\)
      o a < \(\frac{11}{8}\)
      o a < 1 + \(\frac{3}{8}\)

    • Since the number of balls has to be a positive integer, a must be 1.
    • Thus, number of balls in the 5th row = 1 + 4*3 = 13


Thus, option C is the correct answer.

Correct Answer: Option C
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8370
Location: United States (CA)
Re: In a certain supermarket, a triangular display of cans is arranged in  [#permalink]

Show Tags

New post 23 Oct 2019, 19:10
1
Bunuel wrote:
In a certain supermarket, a triangular display of cans is arranged in 8 rows, numbered 1 through 8 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 95 cans in the entire display, how many cans are in the fifth row?

A. 10
B. 11
C. 13
D. 14
E. 16


We can let x = the number of cans in the first row. Thus, x + 3, x + 2(3), …, x + 7(3) are the number of cans in the second, third, …, eighth rows, respectively. Since we have an evenly spaced set, we can use the formula sum = avg * quantity where:

Avg = (largest number + smallest number)/2
Quantity = 8

We can create the inequality:

sum < 95

avg * quantity < 95

(x + 7(3) + x)/2 * 8< 95

(2x + 21)/2 * 8 < 95

(2x + 21) * 8 < 190

16x + 168 < 190

16x < 22

x < 22/16

Since x must be a whole number, x = 1. Therefore, the number of cans in the fifth row is x + 4(3) = 1 + 12 = 13.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: In a certain supermarket, a triangular display of cans is arranged in   [#permalink] 23 Oct 2019, 19:10
Display posts from previous: Sort by

In a certain supermarket, a triangular display of cans is arranged in

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





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