Jack and Mark both received hourly wage increases of 6 perce

Question

Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack' hourly wage was how many dollars per hour more than Mark's?

(1) Before the wage increases, Jack's hourly wage is $5 per hour more than Mark's
(2) Before the wage increases, the ratio of the Jack's hourly wage to Mark's hourly wage is 4 to 3

Source : Sandeep Gupta – Director, Ivy-GMAT

This Q is taken from the source above but the answer is not clear.

Q Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack' hourly wage was
how many dollars per hour more than Mark's?
(1) Before the wage increases, Jack's hourly wage is $5 per hour more than Mark's
(2) Before the wage increases, the ratio of the Jack's hourly wage to Mark's hourly wage is 4 to 3.

PArt (1) Since the question asks only the difference between 2 qty which has undergone   similar percent increase  , the difference between the two will also undergo  same percent increase . so the answer is 5 * 1.06 . SUFFICIENT

Part (2) the ratio b/w 2 qty will remain the same if the 2 qty will have similar percent change. However knowing the ratio will not help us in calculating the difference. so is INSUFFICIENT

Pl Confirm assumptions used in both parts.

Bunuel · Accepted Answer

Yes, your logic is correct. Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack' hourly wage was how many dollars per hour more than Mark's? (1) Before the wage increases, Jack's hourly wage is $5 per hour more than Mark's --> no need for algebra here: as wages increase by 6% then the difference between them also increases by the same 6% --> new difference 5*1.06. Sufficient. (2) Before the wage increases, the ratio of the Jack's hourly wage to Mark's hourly wage is 4 to 3 --> just ratio is not enough to get the value of new difference, as for different hourly wages we'll get different result: bigger the wages the bigger the difference will be. Not sufficient. Answer: A. P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum. Thank you.

AharonU · Answer

Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack' hourly wage was how many dollars per hour more than Mark's?

(1) Before the wage increases, Jack's hourly wage is $5 per hour more than Mark's
(2) Before the wage increases, the ratio of the Jack's hourly wage to Mark's hourly wage is 4 to 3

(1) M before x
 J before x+5
 M after x*1.06
 J after (x+5)*1.06
 J after - M after = (x+5)*1.06-x*1.06 ---> 1.06(x+5-x) ---> 1.06*5 . Sufficient .

(2) M before 3x
 J before 4x
 M after 3x*1.06
 J after 4x*1.06
 J after - M after = 4x*1.06-3x*1.06 ---> 1.06(4x-3x) ---> 1.06*x ---> value of x?. Not Sufficient .

Answer A.

boomtangboy · Answer

Hi,

I dont know if this solution is right or not but made sense to me.... Let me knw if my logic is wrong or not

We need to find Diff =1.06( Jacks' Hourly Wage (J)) -1.06 ( Mark's Hourly Wage (M) )

A ] Sufficient

Diff = 1.06J - 1.06M - Eqn 1
J= M+5 Substitue in Eqn 1 & you get 5

B] Sufficient

J/M = 4/3 => J = 4M/3

You can get a solution for the same as used in A

Therefore D

Hope this helps....

Bunuel · Answer

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EMPOWERgmatRichC · Answer

Hi All,

Ratios show up on a number of questions on Test Day, so it's important to know your ratio rules (and the various 'formats' that ratios can come in). If you don't immediately see the ratio rules that appear in this question, you can still get to the correct answer by TESTing VALUES.

We're told that Jack and Mark each receive a raise of 6% to their hourly wages. We're asked how much larger Jack's hourly wage is AFTER the increases.

Fact 1: Before the increases, Jack's wage was $5/hour more than Mark's wage

IF....
Jack = $10/hour 
Mark = $5/hour
After the raises.....
Jack = 10(1.06) = 10.60
Mark = 5(1.06) = 5.30
So.....Jack's wage is $5.30 more than Mark's

IF....
Jack = $11/hour
Mark = $6/hour
After the raises....
Jack = 11(1.06) = 11.66
Mark = 6(1.06) = 6.36
So....Jack's wage is $5.30 more than Mark's

The result STAYS $5.30 even when the numbers change, so $5.30 is THE difference.
Fact 1 is SUFFICIENT

Fact 2: Before the raises, the ratio of Jack's wage to Mark's wage was 4:3

IF.....
Jack = $4/hour
Mark = $3/hour
After the raises....
Jack = 4(1.06) = 4.24
Mark = 3(1.06) = 3.18
So....Jack's wage is $1.06 more than Mark's

IF....
Jack = $8/hour
Mark = $6/hour
After the raises....
Jack = 8(1.06) = 8.48
Mark = 6(1.06) = 6.36
So....Jack's wage is $2.12 more than Mark's

These two results are DIFFERENT.
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

SherLocked2018 · Answer

1) x and x+5 are the wages. After increase, their wages : 1.06x and 1.06x+1.06*5. Thus diff = 1.06*5. SUFF. 
2) x and 4x/3 are the wages. After increase, their wages : 1.06x and 1.06*4*x/3. Thus diff contains x. Not SUFF.

Ans A. 
(I use symbol x for clarity. No need to calculate the value of x, since we know that by taking the diff, the x term cancels in 1 but remains in 2)

KarishmaB · Answer

An interesting thing to note here is that statement 1 uses the same concept as compound interest. In compound interest, you earn the rate of interest not only on the principal but also on the interest earned till then. We know that Jack's hourly wage is $5 more than Mark. When their wages increase by 6%, Jack earns an extra increase of 6% of $5. So now Jack's wage will be $5+$0.3 = $5.3 more than Mark's wage.

Statement 2 gives us a ratio of wages and not the actual wages. Hence, without any actual number, there is no way we can find the difference in their wages.

BrainLab · Answer

The difference after increases will be: 1.06J-1.06M=1,06(J-M)
(1) Just insert this information (J-M=5 before increases) in the expression above -> 1.06*5 Sufficient
(2) We need a concrete value, the ratio alone is not sufficient
Answer A

grassmonkey · Answer

Ok so two dudes are getting a wage increase, lucky them. We want to know what the difference between their salaries is after the 6% increase.

What are we solving for? Asking yourself that question may seem silly, but it is a really important habit to form, because you need to know what you're looking for in the statements.

1.06*J - 1.06*M = ? 
1.06*(J - M) = ?

Statement 1: Before increase, Jack's salary $5 more than Mark's.

J = M + 5

Almost what we want, just re-arrange:

J - M = 5

Cool, now plug that into the re-phrased question:

1.06*(J - M) = ?
1.06*(5) = 5.3

You've got a value so you can stop (you didn't need to actually work it out)!

Statement 2: Before the increase the ratio of Jack's hourly wage to Mark's hourly wage was 4 to 3.

You might immediately see, as some posters did, that you cannot get a concrete value from a ratio. Mike McGarry had a really good blog post about that I read a while back. Given that the question is asking about a concrete value, and this statement gives you only a ratio, you can just immediate discard this.

Let's just suppose for a moment that you didn't see that, you would do this:

J/M = 4/3
J = (4/3)*M

Ok, try that with our re-phrased question:

1.06*((4/3)*M - M) = ?
1.06*((1/3)*M) = ?

You can't get rid of that M, so you cannot get an actual value to answer the question.

(A)

bumpbot · Answer

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Jack and Mark both received hourly wage increases of 6 perce

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Jack and Mark both received hourly wage increases of 6 perce

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