tax collection inequality ds

Question

The annual tax collected by the government from a certain household was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual tax collected from the household more in 1999 than in 1977?

1) x>y

2) xy/100 < x-y

aikido_fudoshin · Answer

I think E is the answer. Both 1) and 2) give us the same thing : x>y



ex. IT = income tax 

1997 => IT = 80
 > 25% increase x=25
1998 => IT = 100 
 > 20% decrease y=20
1998 => IT = 80 

Add a percentage point to y and the total income tax for 1999 is less than 1997. Subtract a percentage point from y and the income tax for 1999 will be greater than 1997. Therefore both 1) and 2) are insufficient.

allabout · Answer

Are there typos in the stem?

rephrased:
 
A= Value of 1997

What is
A*( 1 + x/100)*(y/100) - A*(1 + x/100)

or

A* 

both statements aren't sufficient

sperumba · Answer

t99 = t98 - y/100 * t98 = t98 (1-y/100)

t98 = t97 + x/100 * t97= t97 (1+x/100)

therfore t99 = t97 * (1+x/100) (1-y/100)

1 . insuff

2. insuff 

1 and 2 Inssuf 

therefore E.

cool_jonny009 · Answer

B

If the diff of the tax in
T97 -T99 = +ve then it was higher in 97 otherwise lower
let say T97 = 100

T98 = 100+x
T99 = (100+x)(100-y)/100

T97 - T99
100 - (100+x)(100-y)/100 = xy/100 - (x-y)

As given in stmt 2 that xy/100 < x-y 
so T97 - T99 = -Ve so the tax in 99 was more than 97

well took me way more than 2 min. 

What is OA ..?

ywilfred · Answer

tax collected in 1997 = a
tax collected in 1998 = b
tax collected in 1999 = c

b = (100+x)/100 (a)
c = (100-y)/100(b)

c = (100-y)/100 * (100+x)/100 * (a)

c = (100-y)(100+x)/100^2 (a)

c = (100^2 + 100x - 100y - xy) / 100^2 * (a)

1) x>y, then 100x > 100y. But not sure if 100x - 100y is greater than -xy

For instance, if x = 2, y =1, then c = (100^2 + 98)/100^2 * (a). Then c < a.

However, if x = 1000, y = 999, then c = (100^2 + 100 - 999,000)/100^2 * (a). Then c > a.

2) We're todl xy < 100x - 100y. So c < a.

Ans B

sperumba · Answer

Thanks ywilfred good explanation.

ps_dahiya · Answer

B

Let Tax in 1997 = 100

Tax in 1998 = 100 + x

Tax in 1999 = (100+x) - (100+x) * y/100
 i.e = 100 + x - y - xy/100

St1: Clearly INSUFF. This is a trap.

St2: if xy/100 0 

Now look at tax in 1999 i.e 100 + (x - y) - (xy/100) will always be greater than 100 if st2 is true.

tax collection inequality ds

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