Search found 111 matches
This has a pretty tough algebraic solution, but see the shortcut at the bottom: m = 2(L + W), "what is m?" Statement 1) LW = 60, so L = 60/W and W = 60/L but it could be that (L,W) is (6,10) and 2(L + W) = 2(16) = 32 or it could be that (L,W) is (5,12) and 2(L + W) = 2(17) = 34 or even tha...
- by goalevan
Wed Aug 10, 2011 6:56 pm- Forum: Data Sufficiency
- Topic: DS Perimeter Question
- Replies: 2
- Views: 1245
If x > -y, then denominator x + y > 0 and the question is "is x - y > x + y"? or "is y < 0?" If x < -y, then denominator x + y < 0 and the question is "is x - y < x + y"? or "is y > 0?" Statement 1) this doesn't reveal the relationship between x and -y, so it'...
- by goalevan
Wed Aug 10, 2011 6:25 pm- Forum: Data Sufficiency
- Topic: x not equal to -y
- Replies: 3
- Views: 1053
d > 0 and 0 < 1 - c/d < 1, so: 0 < (d - c)/d < 1 0 < d - c < d (we can multiply and preserve the direction of inequality since d > 0) c < d < c + d If c + d > d, then c + d - d > d - d, or c > 0. Which of the following must be true? I. c > 0. check, this must be true as shown above. II. c/d < 1. c <...
- by goalevan
Wed Aug 10, 2011 6:05 pm- Forum: Problem Solving
- Topic: Inequalities problem
- Replies: 3
- Views: 1425
S = 20 But S consists of students that scored lower than the mean, equal to the mean, and higher than the mean. L + E + H = 20 L = ? Statement 1) We are given that H = 12, but the students who scored exactly the mean score of 85 are still unknown, so we cannot simply take 20 - 12 = 8, only L + E = 2...
- by goalevan
Sun Aug 07, 2011 3:03 pm- Forum: Data Sufficiency
- Topic: Average
- Replies: 2
- Views: 1184
This would not be sufficient either, since m could still take either an even or odd value. 1) m/2 is NOT an odd integer m/2 = k, or m = 2k, where k is not an odd integer. It is important to understand that k is not necessarily an integer at all. Think of a few values of k that are either even intege...
- by goalevan
Sun Aug 07, 2011 2:29 pm- Forum: Data Sufficiency
- Topic: the special property of even odd integer and non integer
- Replies: 2
- Views: 1409
A^2 + 2AB + B^2 is the sum of squares formula, and equals (A + B)^2:
A^2 + 2AB + B^2
A^2 + AB + AB + B^2
A(A + B) + B(A + B)
(A + B)(A + B)
(A + B)^2
Therefore [A, B] = (A + B)^2
[A, B] = 9
(A + B)^2 = 9
A + B = -3 or 3
- by goalevan
Sun Aug 07, 2011 2:11 pm- Forum: Problem Solving
- Topic: Factoring
- Replies: 2
- Views: 1085
I avoided the quadratic and approximated by taking [(n-2)*180]/n] = 140
180n - 360 = 140n
40n = 360
n = 360/40
n = 9
Then listed the numbers to ensure it worked with 136 as the smallest integer:
136, 137, 138, 139, 140, 141, 142, 143, 144
B
- by goalevan
Sun Aug 07, 2011 2:07 pm- Forum: Problem Solving
- Topic: How many sides?
- Replies: 5
- Views: 2876
1,200(1 + r)^2 = 1,200(1 + 2r) + 132
1,200(1 + r)^2 - 1,200(1 + 2r) = 132
1,200[(1 + r)^2 - (1 + 2r)] = 132
1,200[(r^2 + 2r + 1) - (1 + 2r)] = 132
1,200*r^2 = 132
r^2 = 132/1200
r^2 = (2^2 * 3 * 11) / (2^2 * 3 * 2^2 * 5^2)
r^2 = 11/100
r = sqrt(11)/10
B
- by goalevan
Sun Aug 07, 2011 1:51 pm- Forum: Problem Solving
- Topic: Compound interest problem
- Replies: 4
- Views: 1353
"What is M!/(M - m)! * F!/(F - m)! ?" or "What is M P m * F P f?" To evaluate this quantity, the values of M (the number of males), m (the number of male roles), F (the number of females), and f (the number of female roles) must be known. Statement 1) F = 60% * 50 = 30, so M = 50...
- by goalevan
Sat Aug 06, 2011 5:14 pm- Forum: Data Sufficiency
- Topic: director
- Replies: 7
- Views: 1513
It's easiest to use the variables t and m instead of n: P + I = P(1 + r)^t with one compound per period and t periods. P + I = P(1 + r/m)^(mt) with m compounds per period and t periods. As an aside, when the limit of n to infinity is taken, the quantity (1 + 1/n)^n is equal to the mathematical const...
- by goalevan
Sat Aug 06, 2011 4:47 pm- Forum: Problem Solving
- Topic: Compound Interest Formula
- Replies: 5
- Views: 5031
x ( x - k ) = k + 1
x^2 - kx - k - 1 = 0
x^2 - 1 - k(x + 1) = 0
(x + 1)(x - 1) - k(x + 1) = 0
(x + 1)[(x - 1) - k] = 0
(x + 1)(x - k - 1) = 0
So, either x + 1 = 0, or x = -1, or x - k - 1 = 0, or x = k + 1, (or both).
-1 + k + 1 = k
- by goalevan
Sat Aug 06, 2011 4:29 pm- Forum: Problem Solving
- Topic: 300 tough Algebra
- Replies: 20
- Views: 39561
We are given two equations to begin: M + J = x, and M = J - 80 We can calculate for Joe's current dollars in terms of x: [J - 80] + J = x 2J - 80 = x 2J = x + 80 J = (x + 80)/2 If we add x to both sides, we will have the answer to the question in terms of x on the right side: J + x = (x + 80)/2 + x ...
- by goalevan
Sat Aug 06, 2011 11:19 am- Forum: Problem Solving
- Topic: dollars
- Replies: 4
- Views: 1222
You cannot use one variable to represent both the starting volume and the capacity of the tank, because it is never stated that the tank starts out full. We have to create another variable for the capacity: t, and keep it separate from the starting volume: x. x - 200 = (3/7)t, "what is t?"...
- by goalevan
Sat Aug 06, 2011 11:12 am- Forum: Data Sufficiency
- Topic: capacity of a tank
- Replies: 5
- Views: 1614
We are given that the arithmetic mean is 23 in a set of 7 integers, so the sum of these seven integers is 7 * 23 = 161. The range will be (4x + 15) - x = 3x + 15, where x is the smallest integer in the set. In order to maximize this quantity (the range), we need to maximize the smallest integer in t...
- by goalevan
Thu Aug 04, 2011 5:12 pm- Forum: Problem Solving
- Topic: range question
- Replies: 1
- Views: 973
It's given that x + y = 1 because the type I and type II coffee weigh 1 kilogram together. It's also given that the cost per kilogram C = 6.5x + 8.5y So C = 6.5x + 8.5(1 - x) = 6.5x - 8.5x + 8.5 = -2x + 8.5 x < 0.8? Statement 1) y > 0.15, and x + y = 1, so 1 - x > 0.15, and x < 0.85. x could be less...
- by goalevan
Sat Jul 23, 2011 3:34 pm- Forum: Data Sufficiency
- Topic: One kilogram
- Replies: 2
- Views: 1070