A spreadsheet contains a rectangular block of cells. There a

Question

A spreadsheet contains a rectangular block of cells with 50 more columns than rows. If the spreadsheet were modified by adding 10 columns and removing 5 rows, the total number of cells would remain unchanged. If instead the spreadsheet were modified by adding 20 columns and removing 10 rows, how many fewer cells would the spreadsheet contain than the original spreadsheet?

(A) 50
(B) 100
(C) 200
(D) 300
(E) 500

(A) 50
(B) 100
(C) 200
(D) 300
(E) 500

silviao · Answer

can we have an offical answer pls

kevincan1 · Answer

Suppose the spreadsheet has r rows and r+50 columns. After the first hypothetical modification it would have r-5 rows and r+60 columns

Thus we know that r(r+50) = (r -5)(r+60)

We need to find the difference between  (r - 10)(r + 70) and r(r + 50)

If we expand the first equation, we discover that r=60

So the required difference is is (50)(130) - 60(110) = 100(65 - 66) =-100 (a decrease of 100 cells)

Therefore , the answer is 100.

Dereno · Answer

Rows = r

Columns = 50+r

Given that : adding 10 columns and removing 5 rows, the total number of cells would remain unchanged

row = r-5

column = 50+r+10 = r+60

So, r*(r+5) = (r-5)*(r+60)

solving we get r=60

column = 110.

Total cells = 60*110 = 6600.

case. 2: If instead the spreadsheet were modified by adding 20 columns and removing 10 rows.

Row = 60 -10 = 50

Column = 110 +20 = 130

Total cells = 50*130 = 6500.

Difference in cells = 6600 - 6500 =  100 cells

Option B

Edskore · Answer

Key Concept: Setting Up a System of Equations from Word Problem Constraints

The trap here is trying to answer the final question before fully solving for the spreadsheet dimensions. Most students who get this wrong either skip Step 1 or set up the equation in Step 2 incorrectly. Take it one piece at a time.

Step 1 — Define variables:
Let r = number of rows, c = number of columns.
Given: c = r + 50.

Step 2 — Use the "unchanged cells" condition:
After adding 10 columns and removing 5 rows, total cells = same.
Original: r × c
Modified: (r − 5)(c + 10)
Set them equal:
r·c = (r − 5)(c + 10)
r·c = r·c + 10r − 5c − 50
0 = 10r − 5c − 50
Substitute c = r + 50:
0 = 10r − 5(r + 50) − 50
0 = 10r − 5r − 250 − 50
0 = 5r − 300
r = 60, c = 110

Step 3 — Find the original cell count:
Original spreadsheet: 60 × 110 = 6,600 cells

Step 4 — Apply the second modification:
Add 20 columns and remove 10 rows:
New dimensions: (60 − 10) rows × (110 + 20) columns = 50 × 130 = 6,500 cells

Step 5 — Calculate the difference:
6,600 − 6,500 = 100 fewer cells → Answer: (B)

Common trap: Some students skip Step 2 entirely and try to answer Step 4 directly using the "unchanged" condition as a shortcut. Others set up (r + 5)(c − 10) instead of (r − 5)(c + 10) — mixing up which direction the modification goes. Read carefully: adding columns and removing rows.

Takeaway: Whenever a word problem gives you an "unchanged quantity" condition, that's your equation — set original = modified, expand, and solve. Don't skip to the final question before nailing the dimensions first.

MartyMurray · Answer

A spreadsheet contains a rectangular block of cells with 50 more columns than rows.

Translate

Rows:  r

Columns:  r + 50

If the spreadsheet were modified by adding 10 columns and removing 5 rows, the total number of cells would remain unchanged.

Translate

r(r + 50) = (r - 5)(r + 60)

Solve for r

r^2 + 50r = r^2 + 55r - 300

300 = 5r

60 = r

If instead the spreadsheet were modified by adding 20 columns and removing 10 rows, how many fewer cells would the spreadsheet contain than the original spreadsheet?

Translate and solve

Original:   60 × (60 + 50) = 6600

Modified:  (60 - 10)(60 + 50 + 20) = 6500

Original - Modified:  6600 - 6500 = 100

(A) 50
(B) 100
(C) 200
(D) 300
(E) 500

Correct answer:   B

A spreadsheet contains a rectangular block of cells. There a

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