PWN Test Prep SAT Q&A @pwnthesat - Tumblr Blog

Try (12+x)(16+x)=285, where x is the width of the walkway. :)

If x3 = y, andy > x > 0, then what is the

difference between x6 and x3, in terms of y ?

If x^3 = y, then square both sides to get x^6 = y^2.

From there, we find the difference between x^6 and x^3 by subtracting: x^6 - x^3. Then we just substitute:

x^6 - x^3 = y^2 - y

in the xy plane, the line determined by the points (8,3) and (a,b) passes through the origin. If a isn’t equal to zero, what is b/a ?

When a line passes through the origin, all of the points on the line (other than the origin) tell you the slope. So the answer here is 3/8.

Think of it this way. You can calculate the slope using the two points you know: (0, 0) and (8, 3). Use the slope formula:

(3 – 0)/(8 – 0) = 3/8

That same slope must apply for any other point on the line, like (a, b):

(b – 0)/(a – 0) = 3/8 b/a = 3/8

8 persons paint 8 rooms in 8 days .how many days it will takes 1 man to paint 1 room?

8 days.

The number of boys in a class has increased by 20% compared to the previous year and that of girls has decreased by 20% . There is now one more than before in this class. number of students this year?

You can’t solve this to precisely one number, but you can identify a number of integer solution sets. If this were a real test question it would be worded to say something like “which of the following could be the number of students this year?”

Let’s say the class had b boys and g girls last year.

This year, there’s one more kid in the class, so the total should be b + g + 1.

We also know, however, that the numbers of boys and girls changed: this year there are (1 + 0.2)b boys and (1 – 0.2)g girls.

We can set those two expressions equal and simplify.

b + g + 1 = (1 + 0.2)b + (1 – 0.2)g b + g + 1 = 1.2b + 0.8g 1 = 0.2b – 0.2g 5 = b – g

That’s as far as you can get, so now you’re just left with possible sets that can work. For example, there could have been 15 boys and 10 girls last year, which would mean there are b + g + 1 = 26 students this year.

Any numbers you pick for b and g that are multiples of 5 will give you integer values for the number of boys and girls this year, because multiples of 5 can be increased/decreased by 20% and stay integers.

From the set of integers from 1 to 10 inclusive two integers are randomly selected one after the other with replacement what is the probability that the sum of the two integers are greater than 5

It’s easier to figure out the probability of the sum being 5 or less, and then you can subtract that from 1 to find the answer you actually want.

To get 5 or less, you can only have these two pulls:

1, 1 1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 3, 1 3, 2 4, 1

That’s 10 possible outcomes of 5 or less. Out of how many total outcomes?

Well, you have 10 possible numbers to select, and you’re selecting with replacement, so there are 10*10 = 100 outcomes.

if 10 of them are 5 or less, then there’s a 10% chance of pulling 5 or less. Which means there’s a 90% chance of pulling more than 5.

if x is a positive integer n if there are exactly x+2 integers greater than x and less than x^2 then x

Just do trial and error here.

2^2 = 4, there’s only one integer between 2 and 4.

3^2 = 9, there are five integers between 3 and 5 (4, 5, 6, 7, and 8). So x = 3.

The inequality -6≤x≤3 is a segment graphed on the x axis, and the inequality -4≤y≤8 is a segment graphed on the y axis. What is the area of the quadrilateral formed in the xy plane by joining the endpoint of the graphs?

I knew this one sounded familiar! See here from a couple years ago: https://qa.pwntestprep.com/post/152242806550/the-inequality-6-x-3-is-a-segment-graphed-on

In the triangle ABD shown above, AC bisects angle DAB. Which of the following is equivalent to the ratio AD:DC . A) x:z B) y:z C) z:x D) z:y

figure?

What is the number of cubic inches in 1 foot

I think you mean in a CUBIC foot--you can’t compare cubic inches to feet diresctly.

There are 12 inches in a foot, so there are 12 × 12 × 12 = 1728 cubic inches in a cubic foot.

In the figure above PQRSTU is a regular hexagon. If the area of triangle QSU is root 3, what is the are of the hexagon.

Can you upload an image of the figure? Use the Disqus comments under this post.

#SAT

Three bags of potato chips cost m cents. At this rate, what is the cost, in cents, of one bag of chips.

If three bags cost m cents, then each bag costs one third of that: m/3.

If this isn’t clicking for you, try plugging in a real number for m. Say three bags of chips cost 60 cents. Then each bag must cost 60/3 = 20 cents.

Meredith leans a 15 foot ladder against a wall. The base of the ladder is 4.75 feet from the base of the wall. Of the following, which length,in feet, is closest to the height of the top of the ladder along the wall? A)3.16 B)3.87 C)14.23 D)15.73

This is a right triangle question. The hypotenuse is 15 and the leg on the ground is 4.75. What’s the other leg?

4.75^2 + x^2 = 15^2 22.5625 + x^2 = 225 x^2 = 202.4375 x = 14.22805...

In the xy-plane, the graph of the cubic equation y=x^3+ax^2+bx+c, where a,b, and c are constants, has x-intercept at x=-4, x=-5, and x=-7. What is the value of a?

The x-intercepts tell you the factors, and because the leading term (x^3) has a coefficient of 1 you know there are no constants being multiplied through the whole thing. So you know the factored version of the equation is:

y = (x + 4)(x + 5)(x + 7)

Multiply that out.

y = (x^2 + 9x + 20)(x + 7) y = x^3 + 9x^2 + 20x + 7x^2 + 63x + 140 y = x^3 + 16x^2 + 83x + 140

So a = 16.

How is (-4x^3)^2/3 equivalent to 2x^2(2^1/3)?

Then just rearrange.

Trending Blogs

Recently Viewed Blogs

PWN Test Prep SAT Q&A