‫ אשמח שתפרטו איך‬,‫ מהירויות? אם כן‬3 ‫האם אפשר להשתמש ב"שיטת הציר" גם עבור מקרה של‬
A car traveled the first
of the distance from Town X to Town Y at an
average speed of 20 miles per hour, it traveled the next
of the distance
from Town X to Town Y at an average speed of 30 miles per hour, and it
traveled the final
of the distance from Town X to Town Y at an average
speed of 36 mile per hour. What was the car's average speed, in miles per
hour, when it traveled from Town X to Town Y?
27
28
29
Question Statistics:
19% CHOOSE: 27
8% CHOOSE: 28
59% CHOOSE:
8% CHOOSE: 29
6% CHOOSE:
Sample size = 2,152
Analyze the Question:
While this problem may appear confusing, it is really an Average Speed
problem. Once we isolate which variables go where we can easily solve it.
Identify the Task:
First determine what variables you need and then set up an equation
using the formula for distance and speed.
Approach Strategically:
Since the answer choices are all specified numbers, we know that for any
distance that we select for the distance from Town A to Town B, the
average speed will be the same. Picking Numbers, then, is a perfect
strategy for this problem. Let's try to pick a distance from Town X to
Town Y that is convenient to work with.
Let's select a number of miles for
of the distance from X to Town Y that
is a multiple of 20 miles, 30 miles, and 36 miles. 60 is the least common
multiple of 20 and 30. So now let's find the least common multiple of 60
and 36. 1 × 60 = 60 is not a multiple of 36, 2 × 60 = 120 is not a
multiple of 36, while 3 × 60 = 180 is a multiple of 36 (180 = 5 × 36).
So let's say that
of the distance from X to Town Y is 180 miles. So the
distance from Town X to Town Y is 3 × 180 = 540 miles. The distance
formula is Distance = Speed × Time. We can use this formula in the
rearranged forms: Time =
and Speed =
. The time
that it took the car to travel the first 180 miles was
,
which is 9 hours. The time that it took the car to travel the next 180 miles
was
, which is 6 hours. The time that it took the car to
travel the final 180 miles was
, which is 5 hours. The
total time the car took to travel the 540 miles was 9 + 6 + 5 = 20 hours.
We now have a total distance of 540 miles and a total time of 20 hours.
Now, we can use our Average Speed formula to determine the average
speed of the entire trip:
=
per hour. Answer Choice (A) is correct.
, which is 27 miles
Confirm your Answer:
Remember that if you need to find average speed, you cannot take the
average of two (or three) speeds, because the average will be weighted.
You must find total distance and total time in order to determine this
value..
‫ אשמח שתראו‬,‫צמצום יחסים אולי? אם כן‬/‫האם יש דרך אחרת לפתור את השאלה? בעזרת הרחבת‬
‫איך‬
The only people in each of rooms A and B are students, and each student
in each of rooms A and B is either a junior or a senior. The ratio of the
number of juniors to the number of seniors in room A is 4 to 5, the ratio
of the number of juniors to the number of seniors in room B is 3 to 17,
and the ratio of the total number of juniors in both rooms A and B to the
total number of seniors in both rooms A and B is 5 to 7. What is the ratio
of the total number of students in room A to the total number of students
in room B?
Question Statistics:
21% CHOOSE:
21% CHOOSE:
20% CHOOSE:
30% CHOOSE:
8% CHOOSE:
Sample size = 11,680
Analyze the Question:
This is a ratios question. Our situation is students, classified as juniors or
seniors, in two different rooms, A and B. We are given the ratios of juniors
to seniors in each room and the ratio of total juniors to total seniors. The
question asks for the ratio of all students (juniors and seniors) in A to all
students in B.
Identify the Task:
This is a complicated ratios question, but ratios always give us easily
translatable equations, so if we keep our variables organized and use
those equations, we'll get to an answer.
Approach Strategically:
Picking Numbers is often useful on ratio questions with unknown values,
but it will not help us here, as the only unknown involved is the answer.
As a first step, let's assign a couple of variables. Let's make x the “weight”
of one unit in the ratio for room A. In other words, the number of juniors
in room A is 4x, the number of seniors in room A is 5x, and the total
number of students in room A is 4x + 5x = 9x. Similarly, let's make y the
weight of one unit in room B, so room B has 3yjuniors, 17y seniors, and
3y + 17y = 20y total students. With these variables, we can now reframe
our answer: since we are looking for the ratio of the total number of
students in room A to the total number of students in room B, we want to
find the value of
.
The question stem also gives us a numerical value for the ratio of all
juniors to all seniors (in both rooms), so let's incorporate that into an
equation. We know the ratio of the total number of juniors in both rooms
to the total number of seniors in both rooms is 5 to 7. The total number of
juniors students in rooms A and B is 4x + 3y. The total number of seniors
in rooms A and B is 5x + 17y. Since the ratio of the total number of
juniors in rooms A and B to the total number of seniors in
rooms A and B is 5 to 7, we can write the equation
.
Now, we'll manipulate this equation to help us find . Since we only have
one equation and two variables, we won't be able to solve for x or y, but
we can cross-multiply and simplify to put one in terms of the other, which
will allow us to find the ratio between them.
7(4x + 3y = 5(5x + 17y
28x + 21y = 25x + 85y
3x = 64y
Now that we have x in terms of y, we can substitute into the
expression
to cancel out the ys and turn it into a numerical
expression, which should match with an answer choice. When:
Thankfully, this matches with Answer Choice (D), which is correct.
Confirm your Answer:
There's a lot of math in this question, no two ways about it. The fact that
your calculations yielded a value in an answer choice should be
reassuring, but take a quick glance back to your noteboard to make sure
you didn't make any avoidable mistakes before moving on.
‫או להסביר איך‬/‫ ו‬,‫ נוסחא‬/ ‫ אשמח אם תוכלו לפתור בצורה מפורטת עם טבלא‬.‫לא הבנתי את הפתרון‬
)..."‫לפתור בדרך "בטוחה" אחרת (ההסבר פה נראה כמו "נפנופי ידיים‬
Car X leaves Town A at 2 p.m. and drives toward Town B at a constant
rate of m miles per hour. Fifteen minutes later Car Y begins driving from
Town B to Town A at a constant rate of n miles an hour. If both Car X and
Car Y drive along the same route, will Car X be closer to Town A or
Town B when it passes Car Y?
(1) Car X arrives in Town B 90 minutes after leaving city A.
(2) Car Y arrives in Town A at the same time Car X arrived in Town B.
Statement (1) BY ITSELF is sufficient to answer the question, but
statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but
statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer
the question, even though NEITHER statement BY ITSELF is
sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to
answer the question, requiring more data pertaining to the problem.
Question Statistics:
Test-taker response data for this question is being updated.
Analyze the Question Stem:
This is a special kind of Yes/No question that asks us to determine
whether the answer is “Town A” or “Town B.” We are not asked to provide
a value; instead, for sufficiency, we need to be able to determine whether
the meeting point for two cars is definitely closer to one town or the other.
Being able to determine the speed of each car or their relative speeds
would be sufficient. Remember that speed is a function of distance and
time.
Evaluate the Statements:
Statement (1): This statement does not even mention Car Y, so it must
be Insufficient. Eliminate choices (A) and (D).
Statement (2): This statement tells us that the two cars travel the same
distance to their respective destinations and arrive at the same moment.
Since Car Y starts later, it must travel faster. Now, consider each drive as
a continuum. In the first 15 minutes, Car X travels farther than Car Y,
which hasn’t even started yet. There can be only one moment at which
they have traversed equal distances: the moment when they arrive at
their respective destinations. If they were to keep going past their
destinations, then at any given moment thereafter, the faster vehicle —
Car Y— would have traveled a greater total distance. But Car X must have
traveled farther than Car Y has traveled at any given moment before they
reach their destinations, including the moment when they pass each
other, so the passing point must be closer to Town B (Car X’s destination)
than to Town A. The statement is Sufficient, so the correct answer is
Choice (B).