GRE Mental Math

24*75

1800 12*150 = 6*300 = 1800

7^2 8^2 9^2 11^2 12^2 13^2 14^2 15^2

49 64 81 121 144 169 196 225

If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =

120

115^2

13225 11*12 = 132 13225

56*25

1400 56*25 = 28*50 = 14*100 = 1400

39^2

1521 40^2 = 1600 1600 -40 -39 = 1521

41^2

1681 40^2 = 1600 41^2 +40+41 = 1600 +81 = 1681

List the Prime numbers <20

2, 3, 5, 7, 11, 13, 17, 19

List of Prime Numbers up to 60.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59.

Write fractions in lowest terms 32/48 45/54 52/72

2/3 5/6 13/18

1140 / 5

228 Divide 1140 by 10 -> 114 Double 114 -> 228

55^2

3025 5+1=6 -> 5*6= 30 3025

Which of the following numbers are divisible by 6 but not by 18? Indicate all possible values. 1296; 2744; 3072; 4356; 5832; 6000; 7290; 8112

3072; 6000; 8112;

16,000 has how many positive divisors?

32

260*15

3900 260*15=130*30 = 13*3*10*10 = 39*100 = 3900

84*50

4200 1/2(84) * (50 *2) 42*100= 4200

72-28 86-19 121-72

44 67 49

LCM of 51 & 34

51 = 3*17 34= 2*17 17*2*3 = 102 or LCM = P*Q / GCF 51*34/17 = 3*34 = 102

16*35

560 16= 8*2 (8 X 2) X 35= 8 X (2 X 35) = 8X70 =560

25^2

625 2+1 = 3 -> 2*3 = 6 625

81^2

6561 80^2 = 6400 6400+80+81 = 6561

84^2

7056 85^2 =7225 7225-85-84 = 7140-84 = 7056

69^2

70^2 = 4900 69^2 = 4900 -70 -69 = 4830 -69 = 4761

E*E = E*O = O*O =

E*E = E E*O = E O*O = O

E+/- E = E+/- O = O+/-O =

E+/- E = E E+/- O =O O+/-O = E

Find GCF of 48 and 72

Find the prime factorizations of both numbers, and mark the factors they have in common: 48=2*2*2*2*3 72= 2*2*2*3*3 They both have at least three factors of 2 and one factor of 3, and 2*2*2*3 = 24, so this is the GCF. Answer = 24

If K is the least positive integer that is divisible by every integer from 1 to 8 inclusive, then K =

K= 1*2*3*2*5*7*2

LCM formula

LCM = p*q/GCF You'd never want to perform the multiplication and the numerator first, and then divide. That would be the absolute worst way, the most unintelligent way, to use this formula. You always want to cancel, because of course, the greatest common factor, because it's a common factor, it will cancel both with p and with q.

The most common decimal to fraction conversions include: 0.1 = 1/10 0.125 = 1/8 0.2 = 1/5 0.25 = 1/4 0.33 = 1/3 0.5 = 1/2

So, if you see 0.66, you know that's 2 * 0.33 = 2 * 1/3 = 2/3. Similarly, 0.4 = 0.2 * 2 = 1/5 * 2 = 2/5. If you've got values greater than 1, then you add them as you would a normal fraction. For example: 3.4 = 3 + (2/5) = 15/5 + 2/5 = 17/5 2.33 = 2 + (1/3) = 6/3 + 1/3 = 7/3

x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?

The second condition is more restrictive. We want numbers that, when divided by 23, produce a remainder of 7. We will multiply 23 by integers, starting with zero, and then add 7.23*0 + 7 = 7 23*1 + 7 = 23 + 7 = 30 23*2 + 7 = 46 + 7 = 53 23*3 + 7 = 69 + 7 = 76 23*4 + 7 = 92 + 7 = 99 those five bold numbers are the only five positive integers less than 100 that, when divided by 23, have a remainder of 7. Of those, only one of them also meets the first condition—ending in a 4 or 9, which means that, when it's divided by 5, it has a remainder of 4. Only x = 99 satisfies both conditions, so this is the answer. x = 99

Find Greatest common Divisor 90 & 18

Use prim Factorization 90= 2*3*3*5 18 = 2*3*3 Take common divisors and multiply them together; 2*3*3 = 18 GCD of 90 & 18 = 18

√2

√2 =1.4

Rough approximations for memory √2 √3 √5

√2 =1.4 √3= 1.7 √5= 2.2

√3

√3 =1.7

√5

√5 = 2.2