Company T projected the number of international students studying in t

Question

Company T projected the number of international students studying in the United States (US) for three consecutive school years from 2014–2015 through 2016–2017. The projected numbers for the 2014–2015 school year and during the 2016–2017 school year would be 880,000 and 1,026,080, respectively. Let X % and Y % denote the company’s predicted percentage increase in the number of international students studying in the US from school year 2014–2015 to school year 2015–2016, and from school year 2015–2016 to school year 2016–2017, respectively. Both X and Y are positive integers, and X is less than Y.

In the table, identify the value of X and the value of Y. Make only two selections, one in each column.

In the table, identify the value of X and the value of Y. Make only two selections, one in each column.

MartyMurray · Accepted Answer

Company T projected the number of international students studying in the United States (US) for three consecutive school years from 2014–2015 through 2016–2017. The projected numbers for the 2014–2015 school year and during the 2016–2017 school year would be 880,000 and 1,026,080, respectively. Let X % and Y % denote the company’s predicted percentage increase in the number of international students studying in the US from school year 2014–2015 to school year 2015–2016, and from school year 2015–2016 to school year 2016–2017, respectively. Both X and Y are positive integers, and X is less than Y.

In the table, identify the value of X and the value of Y. Make only two selections, one in each column.

In the table, identify the value of X and the value of Y. Make only two selections, one in each column.

We can see the following:

880,000( 1 + X/100)(1 + Y/100) = 1,026,080

This is one of the few times I'd use the calculator to answer a question to divide 1,026,080 by 880,000 to get 1.166.

So, ( 1 + X/100)(1 + Y/100) = 1.166.

Scanning the answer choices, we can quickly eliminate 20 since 1.2 is already greater than 1.166.

Then, we can note that the only way to get a number that ends in 6 by using the answer choices is to use 6.

And the only numbers we can multiply by 6 to get a decimal that ends in 6 are 6 and 10.

1.06 × 1.06 does not equal 1.166.

1.06 × 1.10 = 1.166

X is less than Y, so the X = 6 and Y = 10

Correct answer:  6 ,  10

Amity007 · Answer

I used the following method.
when 2 consecutive percents are involved then we can use the following formula 
total percent increase can be written as: x+y + x*y/100 
So we found the total percentage as : 1026080 - 880000 = 146080 =>> (146080/880000) x100 =>> 16.60 %
Now if we compare with our formula we can only find 6 and 10 would satisfy the scenario.

FrozenDragon · Answer

Official Answer :

Let A, B, and C be the projected numbers of international students for school years 2014–2015, 2015–2016, and 2016–2017, respectively.

Since A equals 880,000 and C equals 1,026,080, C divided by A equals 1,026,080 divided by 880,000 equals 1.166. So the percent increase from A to C is (C / A - 1) * 100% = 0.166 * 100% = 16.6%.

We now want to find percent increases from A to B and from B to C that yield this 16.6% increase from A to C.

To do this, first note that since C / A = (B / A) * (C / B), it follows that 1.166 = (B / A) * (C / B).

Also note that X is the percent increase from A to B, which is (B / A - 1) * 100%, and that Y is the percent increase from B to C, which is (C / B - 1) * 100%.

Finally, note that we’ve been told that X < Y.

The five answer options 2, 6, 10, 15, and 20 given in the first column, for X, stand for percentage increases of 2%, 6%, 10%, 15%, and 20% from A to B, so these answer options yield the five possible values for B / A of 1.02, 1.06, 1.1, 1.15, and 1.2, respectively.

Likewise, the same five answer options given in the second column, for Y, stand for the same five percentage increases from B to C, so they yield the same five possible values of 1.02, 1.06, 1.1, 1.15, and 1.2 for C / B.

Therefore, since 1.166 = 1.06 * 1.1, the two correct answer options must be 6 and 10.

Since we know X < Y, this gives us answers of X = 6 (corresponding to B / A = 1.06) for the first column and Y = 10 (corresponding to C / B = 1.1) for the second column.

X: The correct answer is 6.

Y: The correct answer is 10.

AbhishekP220108 · Answer

We can solve like this

SInce it was given 880000(1+x%)(1+y%)=1026080

880000(100+x)(100+y)/10000=1026080

(100+x)(100+y)=1026080/88=11660

(100+x)(100+y)=2*2*5*11*53

Since we know X<Y

we can see that

(100+x)(100+y)=2*2*5*11*53 can be written as (100+x)(100+y)=106*110

Hence X=6, y=10

Usernamevisible · Answer

(1 + X/100)(1 + Y/100) = 1.166

Fastest exam shortcut
Notice:
1.166 = 1 + 0.16 + 0.006
For two successive increases:
a% + b% + (ab/100)
must equal 16.6%.
Among choices:
10 + 6 + (10×6)/100
= 16 + 0.6
= 16.6
Immediate match.
Answer: X = 6, Y = 10.

jaykayes · Answer

What they are asking us: Year-on-year % increase over 2 consecutive periods (Y1 to Y2 and Y2 to Y3).

What they are telling us: Absolute values of Y1 and Y3.

First, approximate the values of Y1 and Y3 to the nearest 1000, i.e., 880 and 1026.

We can see that the overall % increase from Y1 to Y3 is 16.6% (using the calculator).
Therefore, the compounded increase of X% and Y% is 16.6%.

Therefore, X% + Y% will be approximately equal to 16.6% but cannot exceed 16.6%.
In fact, X% + Y% must be slightly less than 16.6% because of compounding.

We can immediately eliminate 2, 15, and 20 from both columns, because there is no combination among them that will satisfy the above requirements.

The only remaining question is whether it will be 6 and 10 or 10 and 6.
Since we are told that X is less than Y, we know that X must be 6 and Y must be 10.

kovid231 · Answer

880,000(1+x%)(1+y%)=1026000
(1+x%)(1+y%)=1.1636...

this means the original value when first increases by x% and then by y% gives a value such as 16.36%
hence, the percentage increase must have been like x+y+xy/100 = 16.36%
we can just plug values and see how if x=6 and y=10, we get approx 16 percent.

rishavbatra · Answer

I see this question, as one of compounding. The percentage increase from 8.8 to 10 is a increase OF 16.6%   {approximation}

This 16.6% is equal to X+Y+XY/100 = 10 + 6 + 0.6. Hence, the answer.

Company T projected the number of international students studying in t

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