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3^k+3^k=(3^9)^3^9−3k
3^k+3^k+3^k=(3^3^2)^3^9
3(3^k) = (3)^3^(2+9)
3(3^k) = 3^3^(11)
(3^k) = 3^3^(11)-1
k = 3^(11)-1
- by DrMaths
Thu Jun 14, 2018 3:41 am- Forum: Problem Solving
- Topic: \[ If\ \ 3^k+3^k=(3^9)^{3^9}-3^k,\ \ \ then\ \ \ \ k=? \]
- Replies: 3
- Views: 786
Try reversing the process:
(10 * 2 + 7) * 4./3 = 36
(Note 4/3 is the inverse of 3/4, whereby 1/4 has been removed from 1 whole)
- by DrMaths
Wed Feb 28, 2018 10:50 am- Forum: Problem Solving
- Topic: Bert left the house with N dollars. He spent 1/4 of this...
- Replies: 3
- Views: 828
If x < 20, How many distinct factors does odd number x have? FROM STATEMENT 1: 16x = 2*2*2*2*x 24 = 2*2*2*3 So 16x/24 = 2x/3, means that x is divisible by 3 So x = 3, 9, 15, which gives 2 distinct factors: 3 and 5 FROM STATEMENT 2: 14x = 2*7*x 15 = 3*5* So 14x/15 = 2*7*x/(3*5), means that for non d...
- by DrMaths
Wed Feb 28, 2018 10:44 am- Forum: GMAT Math
- Topic: If x < 20, How many distinct factors does odd number x ha
- Replies: 2
- Views: 3200
Jan: 50 /1.02 = 49.02 Jan last year I will assume that it is the weighted average growth rate you are looking for. Also, based on your question, I assume the growth rates are from last year's (ungiven data) to this year's (given data) revenues. Feb: 75/1.03 = 72.82 Feb last year Mar: 52/0.95 = 54.74...
- by DrMaths
Wed Feb 28, 2018 10:26 am- Forum: GMAT Math
- Topic: Weighted avarage problems with negative numbers and outliers
- Replies: 2
- Views: 3329
X can go in any 3 of 6 boxes, so there are 20 choices for X as follows: XXX000 XX0X00 XX00X0 XX000X X0XX00 X0X0X0 X0X00X X00XX0 X00X0X X000XX 0XXX00 0XX0X0 0XX00X 0X0XX0 0X0X0X 0X00XX 00XXX0 00XX0X 00X0XX 000XXX Of the 3 boxes remaining, for each of the above, Y can go in any 2 of the 3 boxes. So th...
- by DrMaths
Wed Feb 28, 2018 10:08 am- Forum: Problem Solving
- Topic: how many different arrangements can the squares have...
- Replies: 2
- Views: 782
n^2 < 1/100
so n^2 - 1/100 < 0
This is the difference of 2 squares
so (n + 1/10)(n - 1/10) < 0
so n < -1/10 or n < 1/10
However n < 0 (as it is to the left of zero)
so n < -1/10
- by DrMaths
Fri Feb 23, 2018 5:25 am- Forum: Problem Solving
- Topic: If n denotes a number to the left of 0 on the number line su
- Replies: 4
- Views: 1258
If the circle with center O has area 9\piπ, what is the area of equilateral triangle ABC? https://s18.postimg.org/9mlrlj6r9/trianglewithcircle_figure.png I got r = 3 --> d= 6 = AD I tried to solve the problem by calculating CD based on the ratio of a 30-60-90 triangle DC: AD:AC = 1:$$\sqrt{3}$$:2 ...
- by DrMaths
Thu Feb 01, 2018 9:57 am- Forum: GMAT Math
- Topic: Problem solving
- Replies: 2
- Views: 3496
- by DrMaths
Thu Feb 01, 2018 9:35 am- Forum: Problem Solving
- Topic: If the charge of staying in a student youth hostel
- Replies: 4
- Views: 931
- by DrMaths
Thu Feb 01, 2018 9:31 am- Forum: Problem Solving
- Topic: If a≠b, and a2/(a-b)=b, which of the following could be a?
- Replies: 2
- Views: 603
Convert the given facts into equations:
S = 0.52(A+B) = 0.61A + vB (where v = % win in B)
A=3B
Substitute A:
0.52(3B+B) = 0.61*3B + vB
0.52(4B) = 0.61*3B + vB
2.08 = 1.83 + v
v = 2.08-1.83 = 0.25 = 25%
- by DrMaths
Thu Feb 01, 2018 9:22 am- Forum: Problem Solving
- Topic: In an election, candidate Smith won 52 percent of the total
- Replies: 4
- Views: 865
N is divisible by 33, so N = 33*f (where f is an unknown factor) = 3*11*f N^k is divisible by 27, so N^k = 27*g (where g is an unknown factor) = 3*3*3*g = (3^3)*g Combining these 2 facts, we get [3*11*f]^k = (3^3)*g 3^k * (11*f)^k = (3^3)*g Comparing similar bases (namely powers of 3 in this case), ...
- by DrMaths
Thu Feb 01, 2018 9:00 am- Forum: Problem Solving
- Topic: If a number N is divisible by 33, what will be the minimum
- Replies: 3
- Views: 711
- by DrMaths
Thu Feb 01, 2018 8:47 am- Forum: Problem Solving
- Topic: Derek can read x pages in 5 minutes. At this rate, how . . .
- Replies: 3
- Views: 814
Originally: 1/4 @10% + 3/4 @ 10%
Later: 1/4 @ p% + 3/4 @ 10% = 16%
Multiply all by 4:
p% + 30% = 64%
p = 64-30 = 34
Answer = A
- by DrMaths
Thu Feb 01, 2018 8:42 am- Forum: Problem Solving
- Topic: One fourth
- Replies: 3
- Views: 744
x2 + px - 24 = 0
(x+a)(x-b) = 0
ab = 24 -> positive factor pairs (a * b) are 1*24, 2*12, 3*8, 4*6, 6*4, 8*3, 12*2, 24*1
a-b = p = -23, -10, -5, -2, 2, 5, 10, 23
So there are 8 possible values for p
- by DrMaths
Thu Feb 01, 2018 8:36 am- Forum: GMAT Math
- Topic: How many integer values
- Replies: 3
- Views: 3815
8 of these triangles will make an octagon, whose area is 2√2r^2
So 2√2r^2 = 8 * 12
√2r^2 = 48
r^2 = 24√2
Area of circle = pi * r^2 = pi * 24√2
- by DrMaths
Thu Feb 01, 2018 8:22 am- Forum: GMAT Math
- Topic: Great circles question
- Replies: 3
- Views: 3006