Data Sufficiency

Hello, Would like to know if my strategy is correct for the following problem.

A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995.

1. xy=20
2 x+y+(xy)/100 = 9.2

i reworded the question into 1000 + 1000x + (1000+1000x)y =?

1. no help.. elminate A and D
2. simplify to 100x + 100y + xy = 920 . SO here we have 2 distinct equations. solvable.


is this right? I'm curious if i set up the algebra correctly, and im wondering if the XY addds some sort of a twist to the "2 distinct linear equations required for 2 variables" rule.

I setup the equations as
1993 1994 1995
1000 1000(1 + x/100) 1000(1 + x/100)(1+y/100)

the equation for 1995 gives me a term with (x+y) and another in xy
so i additional information for both these terms
Second statement provides me both

fangtray wrote:Hello, Would like to know if my strategy is correct for the following problem.

A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995.

1. xy=20
2 x+y+(xy)/100 = 9.2

i reworded the question into 1000 + 1000x + (1000+1000x)y =?

1. no help.. elminate A and D
2. simplify to 100x + 100y + xy = 920 . SO here we have 2 distinct equations. solvable.


is this right? I'm curious if i set up the algebra correctly, and im wondering if the XY addds some sort of a twist to the "2 distinct linear equations required for 2 variables" rule.

Hi fangtray,

You have the correct solution..
The reason that two equations are not required here is that we are not trying to find the values of 'x' and 'y' individually but rather the final implication of these rises.

Hope it answers you curiosity wrt 'twist'

fangtray wrote:I'm wondering if the XY addds some sort of a twist to the "2 distinct linear equations required for 2 variables" rule.

I just want to address this particular concern, since it's a great question.

Whenever you have a term of two variables multiplied together, you no longer have a linear equation (since when you sub in for x or y, you'll get a squared term).

For example, let's look at this question:

What's the value of x?

1) y - x = -4
2) xy = 32

Isolating y in equation 1, we get:
y = x - 4

and subbing into (2), we get:

x(x-4) = 32
x^2 - 4x = 32
x^2 - 4x - 32 = 0
(x-8)(x+4) = 0
x = 8 or x = -4

So, even though it may have appeared as though we had enough information to solve (and (C) would certainly be the most commonly chosen wrong answer), that "xy" term actually left us with a quadratic with two solutions and the answer would be (E)- not enough information.

So, in general, you should indeed be wary when you see an "xy" (or similar) term in your equations!

fangtray wrote:Hello, Would like to know if my strategy is correct for the following problem.

A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995.

1. xy=20
2 x+y+(xy)/100 = 9.2

i reworded the question into 1000 + 1000x + (1000+1000x)y =?

1. no help.. elminate A and D
2. simplify to 100x + 100y + xy = 920 . SO here we have 2 distinct equations. solvable.1193 10 1995.


is this right? I'm curious if i set up the algebra correctly, and im wondering if the XY addds some sort of a twist to the "2 distinct linear equations required for 2 variables" rule.

The number sold in 1993 = 1000.
To determine the number sold in 1995, we need to know the PERCENT CHANGE from 1993 to 1995.
The correct answer here is easy to see if we have memorized the following formulas:

If a value increases by x% and then by y%:
The total percent change = x + y + (xy)/100.

If a value increases by x% and then decreases by y%:
The total percent change = x - y - (xy)/100.

Question rephrased:
What is the value of x + y + (xy)/100?

Statement 1: xy=20
No way to determine the value of x + y + (xy)/100.
INSUFFICIENT.

Statement 2: x+y+(xy)/100 = 9.2.
Thus, the number of sales increased by 9.2%.
SUFFICIENT.

The correct answer is B.

To see how the formulas above are derived, check my explanation here:

https://www.beatthegmat.com/og-12-q-ds-t77873.html

As per the question we can write following equation for 1995:-

1000(1+x/100)(1+y/100)

For the time being we can remove 1000
(1+x/100)(1+y/100)
and then we can say:-
100^2 + x + y + xy/100

1) xy = 20
So as per our equation
100^2 + x + y + 20/100
But we don't know the value of x+y so insufficient

2) x+y+(xy)/100 = 9.2
So as per our equation
100^2 + 9.2. Sufficient

So choose answer B

1995: (1000+10x)*(1+y/100) = 1000+10x+10y+xy/10

I hope this clarifies. there was a flaw in your reasoning, to do the problem faster.

GMATGuruNY wrote:
If a value increases by x% and then by y%:
The total percent change = x + y + (xy)/100.

If a value increases by x% and then decreases by y%:
The total percent change = x - y - (xy)/100.

To see how the formulas above are derived, check my explanation here:

https://www.beatthegmat.com/og-12-q-ds-t77873.html

GMATGuru, this is a very handy trick! One clarification though - the formulae provided are easy to apply in this question, but for the other question on rent (where you first derived the formulae), if we do not consider plugging in 1997 rent = 100 and straightaway use your formula to compare percent change in 1997 and 1999, would the inequality read:

is 1999 %change > 1997 %change?

Plugging in your formula -

x-y-(xy/100) > 0 ? (Since there was no percent change in 1997)
which simplifies to the eventual x > y+(xy/100)

Does 0 percent change in 1997 make sense in the inequality? I'm confused as to what original value I should compare the percent change to since the question sounds like an inequality question.

Sorry that I'm backdated on this question. Just came across it.

Thanks!

i_have_no_cool_username wrote:

GMATGuruNY wrote:
If a value increases by x% and then by y%:
The total percent change = x + y + (xy)/100.

If a value increases by x% and then decreases by y%:
The total percent change = x - y - (xy)/100.

To see how the formulas above are derived, check my explanation here:

https://www.beatthegmat.com/og-12-q-ds-t77873.html

GMATGuru, this is a very handy trick! One clarification though - the formulae provided are easy to apply in this question, but for the other question on rent (where you first derived the formulae), if we do not consider plugging in 1997 rent = 100 and straightaway use your formula to compare percent change in 1997 and 1999, would the inequality read:

is 1999 %change > 1997 %change?

Plugging in your formula -

x-y-(xy/100) > 0 ? (Since there was no percent change in 1997)
which simplifies to the eventual x > y+(xy/100)

Does 0 percent change in 1997 make sense in the inequality? I'm confused as to what original value I should compare the percent change to since the question sounds like an inequality question.

Sorry that I'm backdated on this question. Just came across it.

Thanks!

Correct! If a value increases by x% and then decreases by y%, the resulting value will be greater than the original value only if x-y-(xy)/100 > 0.

My working:

Let n be the number of cameras produced in 1993.

1993 = n

1994 = nx/100 + x

1995 = [y{n(x+100)}/100]/100 + {n(x+100)}/100

Simplifying the above equation for 1995, we get,

n(xy + 100x + 100y + 10000)/10000

substituting option 2 in the above equation, we get:

n(920+10000)/10000
=> n(.092 + 1)
1.092n.

In my working I am still left out with n. Can someone please correct me? What wrong am I doing?

bubbliiiiiiii wrote:My working:

Let n be the number of cameras produced in 1993.

1993 = n

1994 = nx/100 + x

1995 = [y{n(x+100)}/100]/100 + {n(x+100)}/100

Simplifying the above equation for 1995, we get,

n(xy + 100x + 100y + 10000)/10000

substituting option 2 in the above equation, we get:

n(920+10000)/10000
=> n(.092 + 1)
1.092n.

In my working I am still left out with n. Can someone please correct me? What wrong am I doing?

Maybe because n is already given in the prompt? Read the last line of the prompt, it does mention that 1000 cameras are made in 1993, so your answer is right when you sub n=1000. Right?

Hi,

Thanks .. not sure how I missed that!!!