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Bunuel
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Identical blocks are stacked in rows to create a tower 24 rows tall. 06 Jul 2020, 05:59
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

77% (02:31) correct 23% (02:47) wrong based on 140 sessions

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Identical blocks are stacked in rows to create a tower 24 rows tall. If the top row of the tower consists of four blocks, and each row below the top row consists of eight more blocks than the row directly above it, how many blocks are in the entire tower?

A. 2300
B. 2301
C. 2302
D. 2303
E. 2304
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E
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Identical blocks are stacked in rows to create a tower 24 rows tall. 06 Jul 2020, 06:14
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Bunuel
Identical blocks are stacked in rows to create a tower 24 rows tall. If the top row of the tower consists of four blocks, and each row below the top row consists of eight more blocks than the row directly above it, how many blocks are in the entire tower?

A. 2300
B. 2301
C. 2302
D. 2303
E. 2304
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The blocks are in progression : 4, 12, 20, 28, .......n = 24 terms (in total)
a = 4 and d = 8
Total blocks = \(\frac{n}{2}(2a + (n-1)d)\) = \(12(8 + 23*8)\) = \(12(192)\) = 2304

Hence, OA is (E).
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Identical blocks are stacked in rows to create a tower 24 rows tall. 06 Jul 2020, 06:18
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Bunuel
Identical blocks are stacked in rows to create a tower 24 rows tall. If the top row of the tower consists of four blocks, and each row below the top row consists of eight more blocks than the row directly above it, how many blocks are in the entire tower?

A. 2300
B. 2301
C. 2302
D. 2303
E. 2304
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Number of blocks in row #1: 4
Number of blocks in row #2: 4 + 8
Number of blocks in row #3: 4 + 8 + 8
Number of blocks in row #4: 4 + 8 + 8 + 8
Number of blocks in row #5: 4 + 8 + 8 + 8 + 8
.
.
.
Number of blocks in row #24: 4 + 8 + 8 + 8 + 8 + 8 + 8.......

We want to find the sum of all of the above numbers.
When we add all of the 4's we get (24)(4)

Notice that (24)(4) = (12)(2)(4) = (12)(8), which means (24)(4) is divisible by 8

Since we are adding a bunch of 8's to (24)(4), we know that the final answer must be divisible by 8

When we check the answer choices, we see that only answer choice E is divisible by 8

Answer: E
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Identical blocks are stacked in rows to create a tower 24 rows tall. 06 Jul 2020, 09:09
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IMO E

First(top) row: 4
Second (top-1) row =4+ 8 = 4 + (8*1)
Third (top -2) row: 4 + 8 +8 = 4 + (8*2)
Fourth (top-3) row =4+ 8 + 8 + 8= 4 + (8*3)
Fifth row = 4 + (8*4)
........
last row (24th row) = 4 + (8*23)


Total blocks = 4 + {4 + (8*1)} + {4 + (8*2)} + {4 + (8*3)} + ..... + {4 + (8*23)}
= 4*24 + 8*1 + 8*2 +8*3 .....8*23
= 96 + 8(1+2+3 + ....23)

Sum of n consecutive terms ={n * (n+1) }/2
Sum for (1+2+3 + ....23) = (23* 24 )/2 = 23 * 12

==> Total blocks = 96 + 8*23*12 = 96 + 96 * 23 = 96 (1 + 23) = 96 *24 = 2304
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Identical blocks are stacked in rows to create a tower 24 rows tall. 09 Jun 2024, 02:42
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