Number theory problems

E Test

The digits if a two digit number differ by 4 and their squares differ by 40. Which could be the number ? A) 15 B) 26 C) 40 D) 59 E) 73

D , 23 A/3 = B + (2/3) B/3 = 2 + 1/3 B = (3*2) + 1 = 7 A/3 = 7 + (2/3) A = (3 * 7) + 2 = 23

The number 3 divides A with the result of B and a remainder of 2. The number 3 divides B with a result of 2 and a remainder 1. What is the value of A? A) 13 B) 17 C) 21 D) 23 E) 27

321 -123 321-121= 200 200- 2= 198 E

What is the maximum possible difference between two three digit numbers, each of which is made up by by all of 1, 2and 3? A) 156 B) 168 C) 176 D) 196 E) 198

plug and chug E, 4.8

Which of the following choices does not equal any of the other choices? A) 5.34+4.63-3.24-2.32 B) 5.53+4.73-3.34-2.42 C) 5.53+4.53-3.34-2.22 D) 5.53+4.73-3.24-2.42 E) 5.43+4.73-3.14-2.22

B Just plug and chug 1 + 2 + 3 = 6 6/3=2

Which of the following could be an integer? A) Avg of 2 consecutive integers B) Avg of 3 ? C) Avg of 4 ? D) Avg of 5? E) Avg of 6 and 9

B

Which of the following is divisible by both 2 and 3? A) 1005 B) 1296 C) 1351 D) 1406 E) 1414

Need to divide by 24. Faster mental math would be to break 24 into 20 + 4 (20+4) * 9 180 + 36 = 216

Which of the following is the first number greater than 200 that is a multiple of both 6 and 8? A) 200 B) 208 C) 212 D) 216 E) 224

9 242 - 233

A palindrome number is a number that reads the same forward or backward. For example,787 is a palindrome number. By how much is the first palindrome larger than 233, greater than 233?

D Choose any five even integers 2,4,6,8,10 10-2 = 8

By how much is the greatest of five consecutive even integers greater than the smallest among them? A) 1 B) 2 C) 4 D) 8 E) 10

A

Each of the two positive integers a and b ends with the digit 2. Which of the following does a-b end? A) 0 B) 1 C) 2 D) 3 E) 4

7

How many numbers are there between 100 and 300 inclusive that are multiples of 5 and 6?

Come back and review when learn combinations. For now, Draw a table to represent selection of the digit. Each number is in the column. In column one, cannot use 0 because that would make the number 4 digit so: 2 * 3 * 3 * 3 * 3 ways

How many positive 5 digit numbers can be formed with the digits 0, 3 and 5? A) 14 B) 15 C) 108 D) 162 E) 243

All Test whole numbers and fractions

If 1<p<3, then which could be true? p^2 < 2p p^2 = 2p p^2 > 2p

E Pick a number to solve for. K is best because can approx that total will be near 42, which is 3*14.

If 42.42 =K(14+(m/50), where k and m are positive integers and m<50, then what is the value of k + m? A) 6 B) 7 C) 8 D) 9 E) 10

E

If P and Q are two positive integers and P/Q = 1.15, then P can equal which of the following ? A) 15 B) 18 C) 20 D) 22 E) 23

a+3a=b+3b-4 at first tried (a-b)=(-3a+3b)-4. Got stuck Now solve 4a=4b-4 Divide by 4 a=b-1 a-b=1 pg 203

If a+3a is 4 less than b+3b then a-b= ?

B 1/30

A, B and C are consecutive integers in increasing order of size. If P=(A/5 - B/6) and Q= (B/5-C/6) then Q - P = A) 1/60 B) 1/30 C) 1/12 D) 1/6 E) 1/5

E LCM = 60 Looking to see which of these equations divided by 60 will yield r = 3.

If n is a positive integers which one of the following numbers must have a remainder of 3 when divided by any of the numbers 4,5,6? A) 12n + 3 B) 24n + 3 C) 80n + 3 D) 90n + 2 E) 120n + 3

E Choose 0 as an integer to eliminate A,B and C Choose 1 as an integer to eliminate D

If n is an integer, which cannot be an integer? A) (n-2)/2 B) sq root 2 C) 2/(n+1) D) sqrt (n^2 + 3) E) sqrt (1/(n^2 + 2)

B 28, guess and check

If x is a two digit number. The digits of the number differ by 6, and the squares of the digits differ by 60. Which of the following could x equal? A) 17 B) 28 C) 39 D) 71 E) 93

C

If x, y and z are positive integers such that x<y<z and x + y + z = 6, then what is the value of z? A) 1 B) 2 C) 3 D) 4 E) 5

E LCM = 24 3072/24=3096

The number 3072 is divisible by both 6 and 8. Which one of the following is the first integer larger than 3072 that is also divisible by both 6 and 8? A) 3078 B) 3084 C) 3086 D) 3090 E) 3096

2R

The remainder when positive integer m is divided by n is r. What is the remainder when 2m is divided by 2n? A) r B) 2r C) 2n D) m-nr E) 2(m-nr)

Gave me all variables, just test answer choices. A) 45/7 = 6 + 3/7 R= 3 45/14 = 3 + 3/14 R= 3 nope B) works

The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by 14 is (x+7). Which of the following could m equal? A) 45 B) 53 C) 72 D) 85 E) 100

E

Which of the following equaled the product of exactly two prime numbers? A) 11 * 6 B) 13 * 22 C) 14 * 23 D) 17 * 21 E) 13 * 23

C

Which one of the following equals the product of the smallest prime number greater than 21 and the largest prime number less than 16? A) 13 * 16 B) 13 * 29 C) 13 * 23 D) 15 * 23 E) 16 * 21