2^100 is closest to...? how many integers between 1 & 1000 w/ digit 3 but not 7?

[sassydaddy]

A few 7th grade math questions:

1. If 2^5 = 32, then 2^100 is closest to...

(A) 10^10 . .(B) 10^15 .(C) 10^20 . .(D) 10^25 . .(E) 10^30

2. How many integers between 1 and 1000 contain the digit 3 but not the digit 7?

(A) 171 . .(B) 192 . .(C) 217 . .(D) 235 . .(E) 251

3. What is the largest remnant that can be obtained when a two-digit number is divided by the sum of its digits?

4. Four numbers add up to 58. The following amounts are all equal to each other: the first number plus 1; the second number minus 2; the third number multiplied by 3; and the fourth number divided by 4. If the largest of the four numbers is A and the second largest is B, what is the value of A - B?

(A) 17 . .(B) 19 . .(C) 21 . .(D) 23 . .(E) 25

5. In the sequence 2016, 2013, 2005, 2002, 1994, 1991,..., every number except for 2016 and 2013 is 11 less than some other number in this sequence. Which of these numbers will appear in the sequence?

(A) 1 . .(B) 2 . .(C) 3 . .(D) 5 . .(E) 8

6. The number 123456789 is multiplied by 1001. What is the sum of the digits in the result?

(A) 45 . .(B) 54 . .(C) 63 . .(D) 72 . .(E) 90

Thanks

 

[stapel]

1. If 2^5 = 32, then 2^100 is closest to...

(A) 10^10 . .(B) ^. .(C) 10^20 . .(D) 10^25 . .(E) 10^30

2. How many integers between 1 and 1000 contain the digit 3 but not the digit 7?

(A) 171 . .(B) 192 . .(C) 217 . .(D) 235 . .(E) 251

3. What is the largest remnant that can be obtained when a two-digit number is divided by the sum of its digits?

4. Four numbers add up to 58. The following amounts are all equal to each other: the first number plus 1; the second number minus 2; the third number multiplied by 3; and the fourth number divided by 4. If the largest of the four numbers is A and the second largest is B, what is the value of A - B?

(A) 17 . .(B) 19 . .(C) 21 . .(D) 23 . .(E) 25

5. In the sequence 2016, 2013, 2005, 2002, 1994, 1991,..., every number except for 2016 and 2013 is 11 less than some other number in this sequence. Which of these numbers will appear in the sequence?

(A) 1 . .(B) 2 . .(C) 3 . .(D) 5 . .(E) 8

6. The number 123456789 is multiplied by 1001. What is the sum of the digits in the result?

(A) 45 . .(B) 54 . .(C) 63 . .(D) 72 . .(E) 90

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please reply showing all of your efforts so far. When you reply, please include a correct answer-option for (B) in question (1). Thank you!

 

[sassydaddy]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please reply showing all of your efforts so far. When you reply, please include a correct answer-option for (B) in question (1). Thank you!

I think the answer for 1 is 10^20 but its probably wrong

For number 2, i don't know how to find how many integers between 1 and 1000 contain a 3 to begin with, but wouldnt you do 1000 divided by 3 or something i dont know

For number 3 i have no idea how to find the answer

For number 4 i hate algebra and am too lazy to do it

For number 5 i have no idea how to do it

For number 6 i googled the answer and it was 123580245789 which was a way different answer than the one i thought

 

[JeffM]

This is a HELP site, not an answer site. Our name is Free Math Help, not Free Math Answers.

I must admit, however, that these questions are enough to make anyone hate math.

(1) What in the world do they mean "if 2^5 = 32"? 2^5 IS 32, no ifs, ands, or buts about it. Have you been taught about the laws of exponents or exponents?

(2) Numbers do not have other numbers in them so the question is truly stupid beyond belief. No wonder you are confused. What they are asking is how many integers in the range from 1 through 1000 are represented by decimal numerals that include the digit 3 but not the digit 7. When a problem seems hard, try a simpler problem. Between 1 and 29 how many NUMERALS contain the digit 3? How many of those also contain the digit 7. How about between 1 and 39? How about between 1 and 100?

(3) What is the largest remainder you can get when you divide by two? By three? By four? Do you see a pattern? What are the largest digits you can have in a two digit numeral? What is their sum?

Respond to these, and we can proceed.

 

[Deleted member 4993]

I think the answer for 1 is 10^20 but its probably wrong

32 ≈ 10^(1.5)

 

[stapel]

I think the answer for 1 is 10^20 but its probably wrong

On what basis had you come to this conclusion? What was your reasoning?

For number 2, i don't know how to find how many integers between 1 and 1000 contain a 3 to begin with, but wouldnt you do 1000 divided by 3 or something i dont know...

How many numbers are there, between 1 and 1000? In how many places could those numbers contain a "3"? (You may find it helpful to work with one-digit numbers, then two-digit, etc.) How many of these numbers would not have a "7"?

Work case-by-case.

For number 3 i have no idea how to find the answer

Try using algebra. You've learned about using variables (here). You've learned about translating English into algebraic expressions and equations (here). You've learned about solving equations of various types (such as linear, here). Use this.

Any two-digit number is the sum of a digits (between 1 and 9) multiplied by 10, and another digit (between 0 and 9) in the units place. What variables will you pick for these two unknowns? What expression can you then create? What then would be the expression for their product? Where does this lead?

For number 4 i hate algebra and am too lazy to do it

Okay; then we won't bother with this, either.

For number 5 i have no idea how to do it

What does it mean to be "eleven less than" another number in the sequence? Given the values that they've listed, what do you get, after long division by 11?

For number 6 i googled the answer and it was 123580245789 which was a way different answer than the one i thought

Would we be correct in assuming that, having the answer value, you don't care about how that answer was derived?

Thank you!

 

[Steven G]

A few 7th grade math questions:

1. If 2^5 = 32, then 2^100 is closest to...

(A) 10^10 . .(B) 10^15 .(C) 10^20 . .(D) 10^25 . .(E) 10^30

2. How many integers between 1 and 1000 contain the digit 3 but not the digit 7?

(A) 171 . .(B) 192 . .(C) 217 . .(D) 235 . .(E) 251

3. What is the largest remnant that can be obtained when a two-digit number is divided by the sum of its digits?

4. Four numbers add up to 58. The following amounts are all equal to each other: the first number plus 1; the second number minus 2; the third number multiplied by 3; and the fourth number divided by 4. If the largest of the four numbers is A and the second largest is B, what is the value of A - B?

(A) 17 . .(B) 19 . .(C) 21 . .(D) 23 . .(E) 25

5. In the sequence 2016, 2013, 2005, 2002, 1994, 1991,..., every number except for 2016 and 2013 is 11 less than some other number in this sequence. Which of these numbers will appear in the sequence?

(A) 1 . .(B) 2 . .(C) 3 . .(D) 5 . .(E) 8

6. The number 123456789 is multiplied by 1001. What is the sum of the digits in the result?

(A) 45 . .(B) 54 . .(C) 63 . .(D) 72 . .(E) 90

Thanks

1) Note that 32² = 1024 ~1000=10³
2¹⁰⁰ = (2⁵)²⁰ = 32²⁰ = (32²)¹⁰ ~ (10³)¹⁰ = ....

2) the question is really asking how many 1, 2 or 3 digit numbers has a 3 in it but no 7. Just count them
1 digit numbers: Just 3, so 1 number
2 digit numbers: 13, 23, 33, ..., 63, 83, 93 (so 8 numbers) and 30, 31, 32, 34, 35, 36, 38, 39 (8 more) So 16 numbers
3 digit numbers: The same 17 so far with a 100 or 200 or 400 or 500 or 600 or 800 or 900 added to them. So 7x17=119. Also any number from 300-399 that does not have a 7 in it (100- 19 = 81 more). Total of 200

Total = 1+16 + 200 = 217

numbers that have a 3 in them is not necessarily on the 3 times table.

 

[Steven G]

I think the answer for 1 is 10^20 but its probably wrong

For number 2, i don't know how to find how many integers between 1 and 1000 contain a 3 to begin with, but wouldnt you do 1000 divided by 3 or something i dont know

For number 3 i have no idea how to find the answer

For number 4 i hate algebra and am too lazy to do it

For number 5 i have no idea how to do it

For number 6 i googled the answer and it was 123580245789 which was a way different answer than the one i thought

First the answer to number 6 is NOT 123580245789 as you need to add the digits in this number. 2ndly you can't multiply two numbers when one of the numbers only has 0's and 1's in them? SHAME on you! Less severe you don't know the distributive law? 1001=100 + 1. So multiply the number 12..9 by 1000 (you should know how to do that!) and then multiply 12...9 by 1 (easy enough) and add the two numbers. Then add the digits.