practice test -1 question

[deepeshkumar1991]

A rectangular board is composed of identical squares arranged
in a rectangular array of r rows and r+1 columns.The r rows are numbered from 1 through r and the r+1 columns are numbered from 1 through r+1. If r>10 which of the following represents the number of squares on the board that are neither in the 4th row
nor in the 7th column.

[gmbd97]

This question is tricky and clear clarification of this question requires illustration. Unfortunately this forums does not support illustration.

We are said that this rectangular board consists has r rows ans r+1 columns
1 2 3 4 5 6 7 8 ............r+1
2
3
4
.
.
r
So total number square=r*(r+1)=r^2+r

BUT we asked to exclude 4th row and 7th column
so 4th row has r+1 squares
7th column has r squares
so total squares in both 7th columns and 4th row=r+r+1-1 (Mind it we are counting 1 square twice, so we have to minus that one)
=2r
so total number except 7th columns and 4th row=r^2+r-2r
=r^2-r

And if it is still unclear, don't worry, I hope TOMMY has better idea.
Best Luck!
GM

[tommywallach]

Hey GM,

Nope, you totally nailed it.

Side note, when posting questions, Deepehs, please try to write them as real questions. In other words, give the question and the answer choices, and don't say what the correct answer is. That way, people who see it can try it themselves. Also, answer choices are critical, because there are often methods involving using them as plug-in values, or else ballparking.

Thanks!

-t

[Vasapavan1983]

how the other people really understand the answers with out the diagram in this situation its really confusing..you dont have to draw all the columns but at least an Idea would be make easier

[tommywallach]

Hey Vasa,

Yeah, as I mentioned, this question should not be posted without the answer choices. If I were doing this question, I would simply invent a value for r (r=11 being the best choice). Then you have 11 rows and 12 columns, which is 132 squares. Then there will be 22 squares that aren't in row 4 or column 7 (11 in the row and 12 in the column, but with one overlap, makes for 11 + 12 - 1 = 22).

That makes the "answer" 120 squares. Then you could simply plug 11 in for r in the answer choices.

-t

[aladelokunoladimeji]

Great logic, Tommy

final answer: 110

thank you for the incisive contribution.

Hey Vasa,

Yeah, as I mentioned, this question should not be posted without the answer choices. If I were doing this question, I would simply invent a value for r (r=11 being the best choice). Then you have 11 rows and 12 columns, which is 132 squares. Then there will be 22 squares that aren't in row 4 or column 7 (11 in the row and 12 in the column, but with one overlap, makes for 11 + 12 - 1 = 22).

That makes the "answer" 120 squares. Then you could simply plug 11 in for r in the answer choices.

-t

[tommywallach]

Glad to help!