In a certain brick wall, each row of bricks above the bottom

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

In a certain brick wall, each row of bricks above the bottom

by VJesus12 » Sat Nov 23, 2019 2:33 am

In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

[spoiler]OA=D[/spoiler]

Source: GMAT Paper Tests

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Source: Beat The GMAT — Problem Solving | Sat Nov 23, 2019 2:33 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 23, 2019 7:54 am

VJesus12 wrote:In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

Is working backwards a good way to solve this question?[/quote]
Let x = # of brick in bottom (1st) row
So x-1 = # of brick in 2nd row
So x-2 = # of brick in 3rd row
So x-3 = # of brick in 4th row
So x-4 = # of brick in 5th row

TOTAL # of bricks = 75

So, x + (x-1) + (x-2) + (x-3) + (x-4) = 75
Simplify: 5x - 10 = 75
5x =85
x = 17

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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answer

by [email protected] » Sat Nov 23, 2019 9:56 am

Hi VJesus12,

We're told that in a certain brick wall, each row of bricks above the bottom row contains ONE FEWER brick than the row just below it, there are 5 rows in all and a TOTAL of 75 bricks in the walL. We're asked for the number of bricks in the bottom row. This question can be approached in a number of different ways - and if you recognize the pattern that this question is built around, you can solve it without too much work.

Since each of the 5 rows contains ONE FEWER brick than the row beneath it, we're dealing with 5 CONSECUTIVE integers. The AVERAGE of those 5 numbers will be the 'middle number'.... and with 75 total bricks and 5 rows, that 'middle number' will be 75/5 = 15. Thus, the other 4 rows will be 13 and 14.... and 16 and 17. We now know exactly how many bricks will be in each row, including the bottom row.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Tue Dec 03, 2019 10:02 am, edited 1 time in total.

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Nov 28, 2019 4:24 pm

VJesus12 wrote:In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

[spoiler]OA=D[/spoiler]

Source: GMAT Paper Tests

We can let x = the number of bricks on the bottom row. We can create the equation:

x + (x - 1) + (x - 2) + (x - 3) + (x - 4) = 75

5x - 10 = 75

5x = 85

x = 17

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]