A small business has just invested in a new piece of equipment.

Question

A small business has just invested in a new piece of equipment. The business's accountant estimates that the value of the equipment will decrease over time at a constant rate. Based on this assumption, the accountant properly estimates the value of the equipment 3 years afterward to be $X, 6 years afterward to be $Y, and 8 years afterward to be, for the first time, $0.

Select values for X and for Y that are jointly consistent with the given information. Make only two selections, one in each column.

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ID: 700350

Select values for  X  and for  Y  that are jointly consistent with the given information. Make only two selections, one in each column.

ID: 700350

jeet1204 · Accepted Answer

I think the question to say constant amount rather than constant rate. But we can deduce it means constant amount because ending is 0

Mehul129 · Answer

Take initial value at Year 0 = 800 and negate 100 with each year passing by. Hence, values would be,

Year 1 = 700
Year 2 = 600
 Year 3 = 500 
Year 4 = 400
Year 5 = 300
 Year 6 = 200 
Year 7 = 100
​​​​​​​Year 8 = 0

Elite097 · Answer

KarishmaB  how can constant rate imply absolute value

DhanyaAbhirami · Answer

Let initial value = V
Declining at constant rate r per year
After 8 years, V-8r = 0, r = V/8
After 3 years, V-3r = X => X = 5/8V
After 6 years, V-6r = Y => Y = 2/8V
Y = 2/5X
Only given combination: X = 500, Y = 200

PReciSioN · Answer

The question says constant rate. Not constant percentage rate.

Scholar94 · Answer

While waiting for  KarishmaB 's response, changing at a constant rate implies changing at a contant amount and changing at a constant percentage rate implies an exponential growth rate. So for this question, a contant rate simply means a constant amount

akshatv45 · Answer

Assume initial price as Z and rate of decrease as r.

After 3 years, Z - 3r =. X
After 6 years, Z - 6r = Y
After 8 years, Z - 8r = 0
=> r = Z/8

After 3 years,
=> X = 5Z/8

After 6 years,
=> Y = 2Z/8

We need values that fit such X and Y.

Only possibility from option is X = 500 and Y = 200

Mazbaul95 · Answer

If the value becomes 0 after 8 years, then the constant rate is 100/8=12.5%. 
So, after 3 years, the value is (100%-3*12.5%)= 63.5%
The value after 6 years is (100%-6*12.5%)= 25%.
So, the value after 3 years is 2.5 times the value after 6 years. 
Only viable options are 200*2.5=500.
Answer:
X:500
Y:200

Akshaynandurkar · Answer

first yr
second yr
third yr = x
fourth yr
fifth yr 
sixth yr = y
seventh yr 
eight yr = 0

try to compare x with y
for fourth yr , cost must be 2y
for second yr , cost must be 3y

average of 2y and 3y is the value in third yr which is x
average = 2.5y = x

check options assume y = 200 then x = 2.5x200 = 500
Bingo!
answers are x= 500 and y = 200

Hitesh0701 · Answer

We can deduce that question is implying constant amount rather than constant rate. Because, at the end of 8th year. the value becomes Zero. 
If you are a commerce graduate, you must be knowing that while calculating depreciation on assets via reducing balance method, value can never be zero. there will be some value. (If not sure with this approach, watch reducing balance method with respect to depreciation on fixed assets on youtube, it will be quite clear.)

Let me know if you need more help !

D3N0 · Answer

we know it is decreasing and the ending value is zero so X>Y (must be true)

I started with the minimum value of answer choice in the options for Y, which is 200
that gave me that to be zero in the 8th year decrease has to be 100 per year. With this X can only be 500 (3 years apart) Which is given in the option.

Hence the answer. X= 500 and Y = 200

This is how I approached this. Although it took me some time to properly think through it as I started using rate as in %age and missed the ending value to be zero

(silly mistake)

lavanya.18 · Answer

Please help  MartyTargetTestPrep

Kavicogsci · Answer

KarishmaB  constant rate is considered constant amount here...how come?

KarishmaB · Answer

There is a hint in the question that tells us that we are talking about constant amount (like constant speed), not percentage. 
The value becomes 0 in the 8th year. If we were to use a fixed percentage reduction, the value would never become 0 - it would come close after years, but never 0. If you start with 100 and keep reducing it by 10% every year, when do you hit 0 accurately? Never.

100 * (9/10)(9/10)*(9/10)..................... Does this become 0 ever?

When I read the question, I did assume "rate of depreciation" as in percentage (it is what is practically used too) but once I saw that the value goes to 0, it meant that they are using constant amount. Also, had they been using percentage rate of depreciation, they would need to specify the number of years after which the asset is written off (and its values becomes 0).

vikash905 · Answer

This is very simple question; we need to know depreciation formula which is similar to compound interest formula. Final amount = Initial amount(1-(rate%/100)) ^n. Since, after 8 years final amount is 0, using the formula depreciation rate will be 100%. which means the value will be like this 0---> 100---> 200---> 300---> 400---> 500 and so on. 200 is for 6th year and 500 is for 3rd year counting from back

GMATinsight · Answer

Answer: Option D | A Please check the video for detailed approach and solution https://www.youtube.com/watch?v=EmARrEPC31g Please like the video and subscribe the channel if you like the video. Use 1100+ FREE videos from playlists http://www.Youtube.com/GMATinsight If you like to subscribe to modular courses on Quant and DI then please visit the LINK

PeachSnapple1 · Answer

Slightly caught me off guard at the  6 years afterward  to be $Y...] I was wondering whether they mean 6 more years after the 3 years (so in total 9 years down the road), or they mean 6 years in total. But looking at the number of the answers, I guess it's the former.

ManifestDreamMBA · Answer

I went blank on this and then drew it as a graph and used similar triangle concepts to compare ratio of sides. I know geometry is out but sometimes thinking in geometric terms can be helpful when you run out of options.

Think of X axis as years and Y axis as values
We get 3 points in a right angled triangle at origin
(3,X), (6,Y), (8,0)

Using this,
(8-6)/(8-3)=Y/X
2/5=Y/X

Only 200 and 500 meet the condition

bhanu29 · Answer

Approach using evenly spaced sets or arithmetic progression

an = a + (n-1)d

X = a + 2d --- eq.1
Y = a + 5d--- eq.2

Given a + 7d = 0
d = -a/7

substituting in eq.1 and eq.2
X = a-2a/7 = 5a/7
Y = a-5a/7 = 2a/7

X to Y ratio is 5 : 2
Only numbers that fits this is X = 500, Y = 200 which is the answer

A small business has just invested in a new piece of equipment.

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