If Kyles total post-tax income in 2009 was $64,000, what was his

Question

If Kyle’s total post-tax income in 2009 was $64,000, what was his total post-tax income in 2014?

(1) Kyle’s pre-tax income in 2014 was 50 percent more than that in 2009.
(2) Kyle paid 40 percent more in taxes in 2014 than what he did in 2009.

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Adit_ · Answer

Statement A is not sufficient
Statement B is also not sufficient clearly because at the very least we need 2 equations 
OR
In such questions there could be a trick where combining both the common factor cancels out.

Here, combining both:
1.5PT - 1.4T = ? (PT = Pre tax, T = Tax) 
We know PT - T = 64k (from 1)
Now the only trick being factors canceling out but 1.5 and 1.4 cant be factored out by a common number completely to 1 and thus NOT SUFFICIENT.

Answer: Option E

Dereno · Answer

Post tax income (2009) = $64,000

Post tax income (2014) = ?

Statement 1:

Kyle’s pre-tax income in 2014 was 50 percent more than that in 2009.

Let the pre tax income of 2009 = 2x,

pre tax income of 2014 = 3x

if , 2x yields a post tax income of $64000

then 3x , should yield ⚠️

Is the rates of taxation mentioned as same, if same this approach would apply. But, rates being unclear, the slabs etc, the solution is not possible.

Hence,  Insufficient

Statement 2:

(2) Kyle paid 40 percent more in taxes in 2014 than what he did in 2009.

If the pre tax 2009, 2014 be an and b respectively.

post tax income of 2014 = f

1.4*(a-64000) = (b-f)

Couple of unknowns. Hence,  Insufficient

Combining both statements 1 and 2, we get

1.4* ( 2x - 64000) = (3x -f)

solving ,

f = 0.2x + 6400*14

without knowing x, we cannot find f.

Hence,  Insufficient  .

Option E

egmat · Answer

We know Kyle's  post-tax income in 2009 = $64,000 .
We need to find his  post-tax income in 2014 .

Post-tax income = Pre-tax income − Taxes

Let's use simple notation:
• Pre-tax 2009 = P1, Taxes 2009 = T1
• Pre-tax 2014 = P2, Taxes 2014 = T2
• Given: P1 − T1 = $64,000

Statement 1:  Pre-tax income in 2014 was 50% more than in 2009.
→ P2 = 1.5 × P1

Problem:  We don't know P1 separately, and we don't know T2.
→  NOT SUFFICIENT

Statement 2:  Kyle paid 40% more in taxes in 2014 than in 2009.
→ T2 = 1.4 × T1

Problem:  We don't know T1 separately, and we don't know P2.
→  NOT SUFFICIENT

Combining Both Statements: 
Post-tax 2014 = P2 − T2 = 1.5P1 − 1.4T1

We only know that P1 − T1 = 64,000. This gives us ONE equation but TWO unknowns.

Proof with examples:

Case 1:  P1 = $80,000, T1 = $16,000 → Post-tax = $64,000 ✓
• P2 = $120,000, T2 = $22,400
• Post-tax 2014 =  $97,600

Case 2:  P1 = $100,000, T1 = $36,000 → Post-tax = $64,000 ✓
• P2 = $150,000, T2 = $50,400
• Post-tax 2014 =  $99,600

Both cases satisfy ALL conditions but give  different answers .

Answer: E

Navdeep2000 · Answer

Let the pre-tax income in 2009 be x and Tax be y 
 Accordingly, we are given the post tax income i.e., 
  (x-y) = 64000

Also, let pre-tax income in 2014 be a and Tax be b. 
 So, we have to find  (a-b)=?

(1) Kyle’s pre-tax income in 2014 was 50 percent more than that in 2009.
 It means a=1.5x 
 Clearly, this is  not sufficient  when we plug this in our equations.

(2) Kyle paid 40 percent more in taxes in 2014 than what he did in 2009. 
 Here, b=1.4y 
 Again, this alone is  not sufficient.

(1)+(2) When we combine these together and plug-in accordingly  
 (a-b) = (1.5x-1.4y) 
 We are given that (x-y) = 64000 but on the basis of this, we cannot calculate (1.5x-1.4y). Hence, Not sufficient together.  Option E

ExpertsGlobal5 · Answer

Explanation:  
   
Kyle’s total post-tax income in 2009 = 64000.
  We need to find whether the value of “Kyle’s total post-tax income in 2014” can be determined.  
 
 Statement (1) 
 
Let Kyle’s pre-tax income in 2009 be P.
Kyle’s pre-tax income in 2014 = P + 0.5P = 1.5P 
 
It is NOT possible to determine the exact value of Kyle’s total post-tax income in 2014 from the given information.   Hence, Statement (1) is insufficient.  
 
 Statement (2) 
 
Let the tax paid by Kyle in 2009 be T.
Tax paid by Kyle in 2014 = T + 0.4T = 1.4T 
 
It is NOT possible to determine the exact value of Kyle’s total post-tax income in 2014 from the given information.   Hence, Statement (2) is insufficient.  
 
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements. 
 
 Statement (1) and Statement (2) combined  
 
Kyle’s total post-tax income in 2009 = Kyle’s pre-tax income in 2009 – Tax paid by Kyle in 2009 = P – T = 64000
Kyle’s total post-tax income in 2014 = Kyle’s pre-tax income in 2014 – Tax paid by Kyle in 2014 = 1.5P – 1.4T 
 
 Possibility 1:  If P = 70000, then T = 70000 – 64000 = 6000. In this case, 1.5P – 1.4T = 1.5(70000) – 1.4(6000)
 Possibility 2:  If P = 80000, then T = 80000 – 64000 = 16000. In this case, 1.5P – 1.4T = 1.5(80000) – 1.4(16000)
 
It is not possible to determine the exact value of Kyle’s total post-tax income in 2014.   Hence, Statement (1) and Statement (2) combined are insufficient.  
 
  E is the correct answer choice.

If Kyles total post-tax income in 2009 was $64,000, what was his

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GMAT Data Sufficiency (DS) Questions

If Kyles total post-tax income in 2009 was $64,000, what was his

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