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Here are the 7 bulbs (0 is off, 1 is on) in different (on) combinations that do not include 0000000 (all off):
0000001
0000010
0000011
...etc...
1111111
In binary this is a list of the numbers 1 to 127
(because the next number is 10000000 = 2^7 = 128)
So, quite simply, the answer is 127.
- by Mathsbuddy
Tue Jun 02, 2015 7:45 am- Forum: Problem Solving
- Topic: In how many ways can a room be illuminated if there are 7
- Replies: 8
- Views: 5566
Rewriting as products of prime factors we get:
(16)(20)+ ( 8 ) (32) = (2x2x2x2)(2x2x5) + (2x2x2)(2x2x2x2x2)
= (2^6 x 5) + (2^6 x 4) = 2^6 x 9
SQRT(2^6 x 9) = 2^3 x 3 = 8 x 3 = 24
- by Mathsbuddy
Tue Jun 02, 2015 7:18 am- Forum: Problem Solving
- Topic: Radicals: sqrt((16)(20)+ ( 8 ) (32))
- Replies: 11
- Views: 9911
I like your answer. Nice and simple. The above solution is 100% correct. Of course, we also could have just done some arithmetic. sqrt((16)(20)+(8)(32)) = sqrt(320 + 256) = sqrt(576) = 24 choose (b). Just for kicks sake Stuart: The part inside the square root is a number that ends in 6 (since 16x20 ...
- by Mathsbuddy
Tue Jun 02, 2015 7:10 am- Forum: Problem Solving
- Topic: Radicals: sqrt((16)(20)+ ( 8 ) (32))
- Replies: 11
- Views: 9911
(A) 5x/18
(B) 6x/5
(C) 18x/5
(D) 60x
(E) 3,600,000x
x m/s = y km/h
So y = xm * h / (s * km)
But 1 hour = 60 x 60 seconds = 3600s
and 1km = 1000m
So:
y = xm * 3600s / (s * 1000m)
y = x * 18 /5
ANSWER C
- by Mathsbuddy
Fri Dec 19, 2014 6:48 am- Forum: Problem Solving
- Topic: value speed
- Replies: 5
- Views: 2467
- by Mathsbuddy
Fri Dec 19, 2014 6:42 am- Forum: Problem Solving
- Topic: Interest problem
- Replies: 6
- Views: 3871
In this example, we can see that to travel from Q to P, we go [4,-3]
and to go from P to R, we go [3,4]
Hence line QP is perpendicular to PR.
In other words, QPR is a right-angle triangle.
Using 3-4-5, we also see that QP = PR = 5
So the area is simply 5x5/2 = 12.5
- by Mathsbuddy
Fri Dec 19, 2014 6:32 am- Forum: Problem Solving
- Topic: coordinate geometry
- Replies: 5
- Views: 2690
Height, h = 7 + 70sin60(degrees)
but sin60 = SQRT[3/4]= SQRT[3]/2
So, h = 7 + 70 SQRT[3]/2 = 7 + 35 SQRT[3]
- by Mathsbuddy
Fri Dec 19, 2014 6:25 am- Forum: Problem Solving
- Topic: Geometry Triangle Problem
- Replies: 8
- Views: 2702
- by Mathsbuddy
Fri Dec 19, 2014 4:45 am- Forum: Problem Solving
- Topic: Tricky remainder problem
- Replies: 9
- Views: 14855
For which of the following functions f is f(x)=f(1-x) for all x? A) f(x) = 1-x B) f(x) = 1-x² C) f(x) = x² - (1-x)² D) f(x) = x²(1-x)² E) f(x) = x/(1-x) Let's use the INPUT-OUTPUT approach (aka plug and chug). So, let's use a "nice" value for x. How about x = 0 ? So, we can reword th...
- by Mathsbuddy
Fri Dec 19, 2014 4:34 am- Forum: Problem Solving
- Topic: Help me solve this GMAT Quant Question (GMATPrep) #6
- Replies: 6
- Views: 2758
Both solutions given so far work well. However, you could do them faster by scaling everything down to more manageable figures: Perhaps perimeter = 56 and diagonal = 20 Perhaps perimeter = 28 and diagonal = 10 Perhaps perimeter = 14 and diagonal = 5 The last one here is simplest, by dividing all by ...
- by Mathsbuddy
Fri Dec 19, 2014 4:26 am- Forum: Problem Solving
- Topic: PS: Diagonal of a Rectangle / Area
- Replies: 6
- Views: 3438
Both solutions given so far work well. However, you could do them faster by scaling everything down to more manageable figures: Perhaps perimeter = 56 and diagonal = 20 Perhaps perimeter = 28 and diagonal = 10 Perhaps perimeter = 14 and diagonal = 5 The last one here is simplest, by dividing all by ...
- by Mathsbuddy
Fri Dec 19, 2014 4:24 am- Forum: Problem Solving
- Topic: PS: Diagonal of a Rectangle / Area
- Replies: 6
- Views: 3438
Or put more simply, the only exponent of 5 is 35.Mathsbuddy wrote:(1/5)^m * (1/4)^18 = 1/(2(10)^35)
Find the reciprocal:
5^m * 4^18 =2(10)^35
5^m * 4^18 =2 x 2^35 x 5^35)
5^m * 4^18 =2 x 2^17 x 2^18 x 5^35
5^m * 4^18 =2^36 x 5^35
5^m * 4^18 =4^18 x 5^35
m = 35
- by Mathsbuddy
Fri Dec 19, 2014 4:11 am- Forum: Problem Solving
- Topic: Help me solve this GMAT Quant Question (GMATPrep) #4
- Replies: 7
- Views: 2555
(1/5)^m * (1/4)^18 = 1/(2(10)^35)
Find the reciprocal:
5^m * 4^18 =2(10)^35
5^m * 4^18 =2 x 2^35 x 5^35)
5^m * 4^18 =2 x 2^17 x 2^18 x 5^35
5^m * 4^18 =2^36 x 5^35
5^m * 4^18 =4^18 x 5^35
m = 35
- by Mathsbuddy
Fri Dec 19, 2014 4:09 am- Forum: Problem Solving
- Topic: Help me solve this GMAT Quant Question (GMATPrep) #4
- Replies: 7
- Views: 2555
Consider the equation (x+2)(x+3)/x - 2 = 0 (x+2)(x+3)- 2x = 0 x^2 + 5x + 6 - 2x = 0 y = x^2 + 3x + 6 = 0 This is a U-curve. dy/dx = 2x + 3 = 0 gives a minimum at x = -3/2 Therefore the lowest possible integer is -1 and the highest integer is 4 (from the question the integers are less than 5). This g...
- by Mathsbuddy
Fri Dec 19, 2014 3:52 am- Forum: Problem Solving
- Topic: integer problem
- Replies: 4
- Views: 1668
5^x - 5^x-3 = (124)(5^y)
5^x - 5^x-3 = (125-1)(5^y)
5^x - 5^x-3 = (5^3-1)(5^y)
5^x - 5^x-3 = 5^(3+y)-5^y
y = x - 3
- by Mathsbuddy
Fri Dec 19, 2014 2:57 am- Forum: Problem Solving
- Topic: PS: Exponents
- Replies: 9
- Views: 2772