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Bunuel
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In a certain brick wall, each row of bricks above the bottom row 11 Nov 2015, 00:34
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86% (01:27) correct 14% (01:46) wrong based on 869 sessions

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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
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D
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In a certain brick wall, each row of bricks above the bottom row 11 Nov 2015, 01:05
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Let number of bricks in the bottom row =x
Total number of bricks = 75
Total number of rows = 5
x+ x-1 + x-2 + x -3 + x-4 = 75
=> 5x = 85
=> x= 17

Number of bricks in the bottom row = 17

Answer D
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In a certain brick wall, each row of bricks above the bottom row 11 Nov 2015, 01:41
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Bunuel
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
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HI,
The answer can be taken out by adding up but say a Q with more than 50 rows is there...
in these cases remember...
since the number of bricks are in AP, the average will give us the number of bricks in middle row=75/5=15..
the lowest row will have two more=15+2=17
D
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In a certain brick wall, each row of bricks above the bottom row 17 Nov 2015, 19:12
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let bottom row has x bricks
then,
x+x-1+x-2+x-3+x-4 = 75
5x-10=75
x= 17

Ans:D
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In a certain brick wall, each row of bricks above the bottom row 17 Jun 2021, 06:01
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Here it's given 75 total bricks in 5 rows.
Now 75/5 = 15 , so the first row will be greater than 15 for sure.
We can apply AP sum where sum = 75, rows= n = 5 and difference =1
75 = (5/2)[2*a+ (5-1)*1] where a = first number i.e. the last row of the wall
solving this we get a = 13 , so the first row or the last element of the A.P will be 13+(5-1) = 13+ 4 = 17

So, the answer is D.
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In a certain brick wall, each row of bricks above the bottom row 15 Apr 2022, 16:37
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Bunuel
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
Show more

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question algebraically.
Since both options seem pretty fast, I'll go with testing answer choices

We'll begin with answer choice C, the middlemost answer choice, because we can often eliminated answer choices based on the results of testing the middlemost answer.
(C) 16. This answer choice suggests that the bottom row contains 16 bricks.
This means the row above it contains 15 bricks, the next row contains 14 bricks, the next row contains 13 bricks, and the top row contains 12 bricks.
Add all five rows to get: 16 + 15 + 13 + 12 + 11 = 67, which is no good because we want 75 bricks.
Eliminate choice C. Also, since we need MORE than 67 bricks, we can eliminate choices A and B, since they start off with even fewer bricks than choice C does.

At this point, we need only test one more answer choice. For example, if we test D and it works, we're done. If we test D and it doesn't work, we're still done because the correct answer must be E.

Let's best choice D.
(D) 17. This answer choice suggests that the bottom row contains 17 bricks.
This means the row above it contains 16 bricks, the next row contains 15 bricks, the next row contains 14 bricks, and the top row contains 13 bricks.
Add all five rows to get: 17 + 16 + 15 + 14 + 13 = 75. Perfect!!

Answer: D

-------------------------------

ALTERNATE APPROACH: Apply Algebraic Techniques
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
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In a certain brick wall, each row of bricks above the bottom row 10 Nov 2025, 09:32
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Thanks Brent, great approach
BrentGMATPrepNow


STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question algebraically.
Since both options seem pretty fast, I'll go with testing answer choices

We'll begin with answer choice C, the middlemost answer choice, because we can often eliminated answer choices based on the results of testing the middlemost answer.
(C) 16. This answer choice suggests that the bottom row contains 16 bricks.
This means the row above it contains 15 bricks, the next row contains 14 bricks, the next row contains 13 bricks, and the top row contains 12 bricks.
Add all five rows to get: 16 + 15 + 13 + 12 + 11 = 67, which is no good because we want 75 bricks.
Eliminate choice C. Also, since we need MORE than 67 bricks, we can eliminate choices A and B, since they start off with even fewer bricks than choice C does.

At this point, we need only test one more answer choice. For example, if we test D and it works, we're done. If we test D and it doesn't work, we're still done because the correct answer must be E.

Let's best choice D.
(D) 17. This answer choice suggests that the bottom row contains 17 bricks.
This means the row above it contains 16 bricks, the next row contains 15 bricks, the next row contains 14 bricks, and the top row contains 13 bricks.
Add all five rows to get: 17 + 16 + 15 + 14 + 13 = 75. Perfect!!

Answer: D

-------------------------------

ALTERNATE APPROACH: Apply Algebraic Techniques
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
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