Quant Essentials Flashcards
if a,b,c,d are positive, is a/b = c/d?
1) ad = bc
2) b = d
Equivalent fractions means that ad = bc
e.g. 1/8 = 7/56 -> 1x56 = 8x7
1 is sufficient, 2 is not.
Is 7/9 larger than 6/8?
Yes. Use bowtie method for positive fractions:
for a/b and c/d
if ad>bc
then a/b > c/d
Is 18/23 > 27/32?
No Find a common numerator and compare the denominator.
Larger denom -> smaller fraction
18/23 x 3/3 = 54/69
27/32 x 2/2 = 54/64
What are the DS choices?
A = First alone B = Second alone C = Both together D = Both alone E = Neither together
Split into AD + BCE blocks
1/6 as a decimal?
0.167
1/7 as a decimal?
0.143
1/9 as a decimal?
0.111
0.833 as a fraction?
5/6
When is x^2 < x < sqrt(x)?
When 0 < x < 1.
When x is between 0 and 1, the sqrt(x) is > x, and x^2 is < x
Perfect squares never end in?
2, 3, 7, 8
Because:
1, 4, 9, 25, 36, 49, 64, 81, 100
10011 - 7328 = ?
10011 = 9999 + 12
9999
- 7328
=2671 + 12 = 2683
What is 1/6 as a decimal?
0.167
5/6 = 0.833
What is 0.833 as a fraction?
5/6
0.167 = 1/6
What is 0.143 as a fraction?
1/7
2/7 = 0.286 6/7 = 0.875
What is 6/7 as a decimal?
0.857
5/7 = 0.714
What is 0.571 as a fraction?
4/7
5/7 = 0.714
3/7 as a fraction?
0.429
5/7 = 0.571
What are the positive 1-digit integers?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
REMEMBER 0!
0! = ?
1
If x is not equal to y,
(x-y)/(y-x) =?
(x-y)/(y-x) = -1 (x-y)/(-1)(x-y) = -1
What are the 25 prime numbers less than 100?
2, 3, 5, 7 11, 13, 17, 19 23, 29 31, 37 41, 43, 47 53, 59 61, 67 71, 73, 79 83, 89 97
How many different positive integers are factors of 12,000?
- Find the prime factorization
12,000 = 2^5 x 3^1 x 5^3 - Add 1 to the value of each exponent, then multiply.
Total number of factors = (5+1)(1+1)(3+1) = 48
If we know the LCM and GCF of two positive integers (x,y), we know their product.
x * y = LCM (x,y) x GCF (x,y)
e.g. If LCM = 24, GCF = 2,
then, xy = 24 * 2 = 48
Divisibility rule for 3
If sum of all digits is divisible by 3