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

Question

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

shridhar786 · Accepted Answer

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

Archit3110 · Answer

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

hemantbafna · Answer

(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

Pritishd · Answer

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

Basshead · Answer

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.

DeeptiManyaExpert · Answer

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.

Karan0912 · Answer

Is there a way to evaluate Statement 1 with just logic without picking up a pen?

SudsMeister · Answer

Shouldn't the Q stem mention the relationship between cents and $? Or does the GMAT expect a candidate to know it?

Bunuel · Answer

When necessary, the question itself will supply the relative conversions. Though you should have a few basic ones memorized: 1 hour = 60 minutes, 1 dollar = 100 cents, ...

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

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GMAT Data Sufficiency (DS) Questions

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

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