How many positive integers less than 50 are equal to the sum of six consecutive positive integers?
A)Four
B)five
C)six
D)seven
E)eight
should i try from 1 to 6 then from 2 to 7 etc or there is another way?
A recipe for hot cereal requires 1/2 cup of dry cereal to be mixed with 3/4 cup of milk.By mistake 3/4 cup of dry cereal was mixed with 1/2 cup of milk.what fraction of cup of milk should be added to the mixture so that the ratio of cereal to milk will be the same as required by the recipe?
In the figure above a wooden cube is cut into two pieces by making a slice through the midpoints of four of edges of the cube. the volume of the smaller piece is what fraction of the volume of the original cube?
from the point O with coordinates (0,0) on an xy coordinate grid point P is located 3 untis down and 4 units to the right.what is the slope of the line that contains points P and O?
A)-4/3
B)-3/4
C)1/5
D)3/4
E)4/3
why is it E not D isnt it rise over run?
the amounts wanda earns is directly propotional to the number of hours she works.if she earns d dollars per hour and works for h hours,how much does she earn in dollars in terms of d and h?
A) dh
B )h/d
C)d/h
D)h-d
E)d-h
there is another question i need…i cant understand it but it has a graph so i think the graph is needed to answer the question…can i say which test and which number?
Well, you could establish when six numbers equal 51. That is an easy step if you consider the numbers 8 and 9. If they were to be the median numbers of a series of 6, that series would total 3x17 or 51. Try it and you will see. You should spend some time understanding such concept. For instance, if 5 is the median of a series of 5 numbers, the total of the series would be 5 x 5 or 25.
From there you know that a series starting at 6 (namely 6 7 8 9 10 11) totals 51. All the smaller ones will work and this gives you the correct answer.
@xiggi in the first question i understood the concept but i still didnt get from where u got the numbers like how will i know that if the median was 9 and 8 it will be 51
the second one seems easy but idk why i dont get it…why is the ratio 3/2 shouldnt it be 2/3?..that 9/8 u got is for what?
@CrazinessISlife I don’t understand what you are saying, and you seem to have mixed up the rules.
In general, if f(x) is a function in x, and a > 0, then the graph of f(x+a) is obtained by shifting the graph of f(x) a units to the left. This is because, if (x0, y0) is a point on f(x), then f(x+a) maps the point x0-a to y0.
But in this case, we are only moving a single point 4 units to the right and 3 units down.
I think it’s worth pointing out that this “Wanda” problem can be easily solved by making up numbers. For students who feel a little shaky with traditional algebra, this is often the best bet:
the amounts wanda earns is directly propotional to the number of hours she works.if she earns d dollars per hour and works for h hours,how much does she earn in dollars in terms of d and h?
A) dh
B )h/d
C)d/h
D)h-d
E)d-h
Say she makes d=7 dollars per hour and she works for h=4 hours. In that case, she would make $28. Then put those same made up numbers into the answers and rule out anything that does not come out equal to $28.
Those of you who immediately “see” the algebra may dismiss this as more effort than necessary. But I think it is nice to have a safe, easy way to attack these.
In fact, the first sentence is almost unnecessary. This “confusion” over what “directly proportional” means is not necessary in terms of solving the problem (although it is good to know what “directly proportional” means). Plugging in numbers for d and h is not a bad idea if you have a weak algebra background.
Let n be the first positive integer of the 6 consecutive integers (n>0). The 6 consecutive integers will be: n, n+1, n+2, n+3, n+4, n+5.
Their sum is: 6n + 15. Each value of n has exactly 1 equivalent value of the sum.
We also have: 6n + 15<50 => n<5.83 => n can be 1, 2, 3, 4, 5 => B.
@Synonyms thanks alot = )
but number 3 the answer is not 1/2 it said “by making a slice through the midpoints of four of edges of the cube”
it made a slice in the midpoint of the down edge and the parrallel edge above it…and in the adjacent side the same…so it looks like a triangle from above…got it or no?
@Synonyms no problem am not a native speaker too
lets name the 8 vertices of the cube as u said ABCD A1B1C1D1
we have 2 midpoints on each side
make a line from the midpoint of the edge of AD to the midpoint of the adjacent side DC (the edge not the side)
then do the same down
a line from the midpoint of the edge A1D1 to the midpoint of the adjacent side D1C1
now do a line from the midpoint of AD TO THE MIDPOINT OF A1D1 and the same in the other a lline from the mispoint of DC TO the midpoint of D1C1
so it looks like 2 triangles and three rectangulars shape.
if u still didnt get it tell me no problem
