Jesus Christ

For the second problem, x = 50y + 69. y must be even. If it were odd, then x would be even.

The way I see it, the only possible answers are 13 and 5, neither of which options. Are you sure it is not between W and Z? It would make more sense.

(I) Counter example. If the units digit of a is 5 and the units digit of b is 5 then the units digit of a + b will be 0. So (I) is false. (II) Since the tens digit of a is 8, this will be true. The highest the tens digit of b can be is 9 and it has to be greater than 2. Suppose it's 9. Then the tens digit of a + b will be 7 plus a possible 1 carry over from adding the ones digit. Clearly 9 is not attainable, unless the ones digit of b is 0 or 1, which is restricted. True. (III) is true. It follows that if b + a > 1000 and b > a, then b + b > 1000 and b > 500. So my answer is D

The trick here is basically to identify that 2/2^m = 1/2^(m-1). If you know that you are golden.

This is a tricky questions because it deals with time series data. For 1992 there are 6 data points which means to get the meadian we should look at the 3rd and 4th highest values, not the 3rd and 4th months. The 3rd and 4th highest values happen in Aug and October and both have a value of 6500 (approx), thus the median in 1992 is 6500. They trick you here because in 1993 there are 7 data points, so we need to look at the 4th highest value which happens to also be the 4th month in the year, or 6000. So the anwere is 500 less. When calculating medians, time is irrelevent.

This looks a little suspect. They first leave the radical out and then in the second line they put it back in, but they have a 2 under the radical. I'd say it is an error.

Interesting. The prime factorization of 30 is 2*3*5. To be divisible by 12 we need another 2* in the front of this thing, which will only happen with the even multiples. Since there are 12 total integers that satisfy the first condition, I deduce that half of them are divisible by 12, namely 60, 120, 180, 240, 300, and 360. Another way to do this would be brute force, since there are only 12 options.

7x + 3y = 12 3x + 7y = 6 Subtract the second from the first... (7x + 3y) - (3x + 7y) = 12 - 6 Notice since 3x + 7y = 6, we subtracted the same number from each side so the equality still holds. Simplifying gives you 4x - 4y = 6... dividing both sides by 4 gives you x - y = 3/2.

Just use an example. Let c = 12 and d = 18. Then m = 6. gcf of c + d = 30 and 12 is 6. gcf of 2 + d = 20 and 12 is 4. gcf of cd = 216 and 12 is 12. gcf of 2d = 36 and 12 is 12. gcf of d^2 = 324 and 12 is 12. So the only answer is A.

You need the prime factorization of each. 1000 = 2*2*2*5*5*5 68 = 2*2*17 So the greatest prime factor of 1000 is 5 and the greastes prime factor of 68 is 17.

If BC went through the center of the circle then x would = 90. It specifically says that it's not the diameter, so we know x 90. We do not know the position of BC. if the center of the circle is between A and BC then x 90. What is important in this question is to not make any assumptions based on the scale of the drawing. From the picture, it certainly appears that BC lies between A and the center which would lead us to believe that x > 90, but notice that underneath the drawing it says "Figure not drawn to scale" so we cannot make this assumption.

Good catch! They fooled me. 43/60 is correct. In my formula, just switch the (2/3) and the (1/3).

(2/3)*(75/100)+(1/3)*(70/100) = 220/300 = 11/15

Adding to the second part of my reply, the question is probably not best looked at as a combination question, but you COULD do the following if you really wanted to: Total combinations of 2 students from 2-year community colleges: 34!/(2!(32!)) = 561 Total combinations of 2 students from all 100 students: 100!/(2!(98!)) = 4950 Then the probability is 561/4950 = 17/150

((1/10)+1/(1/10))(1/(1/10))= 10.1 * 10 = 101 34/100 * 33/99 = 1122/9900 = 17/150 34/100 is the probablilty that the first selected student came from a 2-year community college. Now that one student has been selected, there are only 99 left and 33 2-year community college transfers, so the probability of the second selected student being from a 2-year community college is 33/99. These are independent events, so you can mulitply them to get the total probability.

Agreed.

1. The Range is 4 so x or x squared must be 5 (or -4, but x>0 so this doesn't work) since 1 is the lowest number and 5-1 = 4. If x = 5 then x^ = 25, which would result in a range of 25 - 1 = 24. This means x^2 = 5 thus x = 2.24 so A is the answer. 2. Plug 3 in for x and get 9 + 3k - 6 = 0. Now solve for k and get k = -1. A root is a a value of x that sets the equation equal to 0, so we know that if you plug 3 in for x the equation will hold. 3. First order them and get 8 8 8 8 10 10 10 10 11 12 12. Now notice that whatever the value of y is (assuming it is an integer) will result in the 6th and 7th numbers being 10, thus the median is 10.

I don't agree with Rezwan. Even if there are an infinite number of shipments, it would still cost at most $0.20 per ounce which would be 25*16*0.20 = $80. Is there a unit on the 576? Is it $576? One this I noticed was that 24*16*0.15 = 57.6. There might be a typo in this question, either in the book or in your transcription.

You can use your approach, but I think you are not understanding the question right. (8/18) + x = 5/6 is the formular you should start with. You are adding x to the 8 oz already in the glass. When you solve you get x = 7/18. So you are adding 7 oz. I would look at it a different way. If an 18 oz glass is 5/6 full then there is (5/6) * 18 = 15 oz of fluid in it. You started with 8 oz so you know that 15 - 8 = 7 were added.

1. Solve 0.15A + 0.5B = 1.2 and A + B = 4. We have 1.2 on the right side of the first equation because you need to get a 4 gallon mixture of 30% alcohol and 0.3*4 = 1.2. 2. Same idea, solve 0.1A + 0.35B = 250 and A + B = 1000. 3. You have 0.4*3 + 0.5*1 = 1.7 liters of orange juice in a 4 liter mixture, so 1.7/4 = 0.425. 4. Same idea as 3, you have 0.4*7 + 0.2*18 = 6.4 liters of water in a 25 liter mixture, so 6.4/25 = 0.256. 5. Solve 0.6(4+y) = 1 + 0.8y for y and get y = 7. I'll do the rest later, have to go to a meeting.

5 is wrong. The answer should be 7. Solve 1 + 0.8y = 0.6(4 + y) for y and get 7. I agree with the rest of your answers.

Annabel's approach is the way you should tackle these problems. Resort back to the equations you know and modify them as the problem describes. In this case, you know the original area is L x W = A. You then need to rewrite this formula to represent the changes the problems describe. Length increases by a factor of 2 so instead of L you have 2L. Similarly, you have 6A. You can call the increase on W as n and then form the equation 2L x nW = 6A. All that's left is to solve for n.

Agreed. One thing to realize here is that STD is based on the mean and if you subtract 10 from the integers in quantity B you are left with the exact same type of quantity as you see in A.

Here is some brief work. Not complete explanations though. 1. You only need to worry about the last 2 digits in each number. 66*78 = 5148 and 4 + 8 = 12. 2. 1.5S = 1.5 K/T = K/[(1/1.5)T] = K/[(2/3)T] so if you increase S by 50% you need to decrease T by 33%. 3. 7 workers * 7 Days = 7 cars, thus 1 worker * 7 Days = 1 Car (divided each side by 7). Therefore, mutiply each side by 5 and you get 5 workers * 7 days = 5 cars. 4. 6 workers * 2 days = 4 cars, thus (8/6)*6workers * 2 days = (8/6)*4 cars, thus 8 workers * 2 days = (16/3) cars, thus 8 workers * (18/16)*2 days = 6 cars, thus 8 workers * 9/4 days = 6 cars. 5. From the first piece of information we know that n = 27, 32, 37, 42, or 47. From the 2nd piece of information we can reduce our possibilities to n = 37. And if she has 37 pieces, she will give each of the 5 children 7 pieces and has 2 remaining. 6. 225 = 3^2*5^2 and 216 = 2^3 * 3^3. You want to take the largerst exponent of each to ensure that the number is divisible by both, so a = 3, b = 3, and c = 2. Therefore a + b + c = 8. 7. There are 6 of them so there are 6! ways to seat them or 720. Now, Ann and Bea can sit next to each other in seats 1 and 2, 2 and 3, 3 and 4, 4 and 5, and 5 and 6 or 5 ways, but we can have Ann on the left of Bea or Ann on the right of Bea so there are 10 different configurations. If they are next to each other we can arrange the other 4 in 4! different ways or 24 ways. 24*10 =240 that we want to elimintate. 720 - 240 = 480. 8. Tricky question. It is divisible by any p^n*q^m where n and m are integers with values = 0. So you have 4 options for the exponent on p (0,1,2,3) and 7 options for the exponent on q (0,1,2,3,4,5,6). This gives you 7 * 4 = 28 different combinations. 9. Another tricky question. Think of the different ways to get there: One 5 all 0's, one 4 and one 1, one 3 two 1's, one 3 one 2, one 2 three 1's. One 5 can happen 4 ways. One 4 and one 1 can happen 12 ways. One 3 and two 1's can happen 12 ways. One 4 and one 2 can happen 12 ways. One 2 and three 1's can happen 4 ways. so 4 + 12 + 12 + 12 + 4 = 56.

1. Solve 0.1 * x + 0.35 * y = 250 and x + y = 1000. When you solve that system you get y = 600 and x = 400. 2. You can just do a weighted average here: (3*0.4 + 1*0.50)/(3+1) = 1.7/4 = 0.425. 3. Again, weighted average: (7*0.4 + 18 * 0.2)/(7+18) = 6.4/25 = 0.256 4. Solve (4*0.25 + x*0.8)/(4+x) = 0.60 and get x = 7. Notice this is just the weighted average formula. 5. If 40% is vinegar then there are 4.8 ounces of vinegar in the mixture and 7.2 ounces of oil. So solve 4.8/(7.2+x)=0.25 and get 7.2.