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State X has a sales tax rate of k percent on all purchases and State Y

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gmatt1476
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State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   21 Sep 2019, 16:40
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State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.


DS08402.01
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A
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shridhar786
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State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   22 Sep 2019, 11:03
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State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

STATEMENT (1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
The sales tax on a $15 purchase in country X = \(\frac{15k}{100}\)
The sales tax on a $15 purchase in country Y = \(\frac{15n}{100}\)
\(\frac{15k}{100}\)-\(\frac{15n}{100}\) = 0.3
k-n = 2
SUFFICIENT

STATEMENT (2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.
K = 1.4n
from this k-n can have different values
we cant find the definite value of k-n
INSUFFICIENT

A is the correct answer
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Re: State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   14 Jun 2020, 10:58
gmatt1476 wrote:
State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.


DS08402.01


target is find k-n

#1
The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
1500/100*k - 1500/100 * n = 30
k-n = 2
sufficient
#2
The sales tax rate in State X is 1.4 times the sales tax rate in State Y.

k/100= 1.4*n/100
k=1.4n
value of k & n cannot be determined ; insufficient
OPTION A
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Re: State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   04 Aug 2020, 01:39
gmatt1476 wrote:
State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.


DS08402.01


(1)15(k/100)-15(n/100)=0.30
Therefore exact value of k-n can be calculated.
Sufficient.

(2) k=1.4(n)

Different values of k and n are possible.
Not sufficient.

A
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State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   10 Oct 2020, 10:44
gmatt1476 wrote:
State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.

DS08402.01

1. Rate in state \(X\) is k% or \(\frac{k}{100}\)
2. Rate in state \(Y\) is n% or \(\frac{n}{100}\)

Statement-I (Sufficient)
\(\frac{k}{100}*15 + \frac{n}{100}*15 = 0.30\) -> \(\frac{15}{100} * (k-n)\) \(= \frac{30}{100}\) -> \(k-n = 2\)

Statement-II (Insufficient)
\(k = 1.4n\), but this is not helpful to derive \(k-n\)

Ans. A
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State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   10 Nov 2020, 17:20
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State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.

let \(\frac{15k}{100}\) = tax on k
let \(\frac{15n}{100}\) = tax on n

\(\frac{15k}{100}\) - \(\frac{15n}{100}\) = 0.30
\(15k - 15n = 30\)
\(k - n = 2\)

SUFFICIENT.

(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.

Clearly insufficient.

Answer is A.
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Re: State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   02 Feb 2021, 23:19
Know: X --> @k%
Y --> @n%

Find: k - n = ?

Need: k, n

1) \(\frac{k}{100}\) x 15 - \(\frac{n}{100}\) x 15 = 0.30
0.15 (k - n) = 0.30

[You will get the value of k - n. No need to solve the equation. This is a DS question]

SUFFICIENT

2) k = 1.4n

[This is not helpful. Won't give k - n.]

INSUFFICIENT

Hence, the answer is A.

Remember, it is important to write the equations down on the DS questions.

Hope this helps. :)
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Re: State X has a sales tax rate of k percent on all purchases and State Y [#permalink] New post   11 Aug 2023, 09:03
Is there a way to evaluate Statement 1 with just logic without picking up a pen?
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Re: State X has a sales tax rate of k percent on all purchases and State Y [#permalink]
11 Aug 2023, 09:03
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