If Jim earns x dollars per hour, it will take him 4 hours to

Question

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

Aj85 · Accepted Answer

It is given tom earns X $ per hour and it takes him 4 hrs to purchase the jacket. so price of jacket 4x $. Now jim earns Y and it takes him 5hrs to earn enough to buy the jacket. So jacket's price = 5y.

so 4x= 5y thus x= 5y/4.

(1) Insufficient. - It is a redundant information. The question stem already gives the relation between x and y.

(2) sufficient - x + y = 43.75, so substitute the value of x for y. 5y/4 + y =43.75 >> 9y= 43.75 * 4 >> the price of jacket is 5y , so price = 43.75* 5*4 /9 = 875/9 $

B is the answer.

KarishmaB · Answer

You can also use ratios here to arrive at answer (B) in moments.

Time taken by Jim : Time take by Tom = 4:5
Hourly rate of Jim : Hourly rate of Tom = 5:4 = x:y
(Since Money Earned = Hourly Rate * Time and Money to be earned is the same for both Jim and Tom)

Statement 1: We already know that hourly rate of Tom is 20% less than the hourly rate of Jim (because it is in the ratio 5:4). No information about actual dollar amount so not sufficient.

Statement 2: On the ratio scale, x+y is 9 but it is actually 43.75. So we can get the values of x and y and hence can find the cost of the jacket. Sufficient. 
Answer (B)

Note: You don't need to calculate the cost of the jacket. You just need to say whether you can calculate it.

jamifahad · Answer

Jim's rate x dollar/hour.
Tom's rate y dollar/hour

Money made by Jim in 4 hours = Money made by Tom in 5 hours
=> 4x=5y----(1)

Stmt1: y=x-0.2x => y=0.8x
Put in (1) => 4x=4x. Same equation. Not sufficient.

Stmt2: x + y = $43.75 
Also, 4x = 5y.
Two equation , two unknown. Sufficient.

OA B

Warlock007 · Answer

B For me as A and the information given in the question are same B give an additional equation which is required to solve for the values I wish these types of questions come in my real GMAT.......

Spidy001 · Answer

Jack - $x/hr

has to work 4 hours to be able to buy a jacket = $4x spent on the jacket

Tom - $y/hr

has to work 5 hours to be able to buy the same jacket = $5y spent on the jacket

=>4x=5y=?

1. Not sufficient

y =(80/100)x => y =4x/5=>5y =4x
 
 which is exact same equation

2. Sufficient
 we can solve this equation and equation in the stem to get the jacket price.

Answer is B.

GyanOne · Answer

4x = 5y
=> x/y = 4/5

Statement (1) just restates this fact, so nothing new here. Insufficient. 
Statement (2) gives us another equation in x and y which we can solve to find x (or y) and calculate 4x or 5y. Sufficient.

(B) it is.

calreg11 · Answer

+1 B
solve for x and solve for y. x = price of jacket / 4 and y = p/5.
when you know the relative rates of x and y they only tell you what p equals each other... 
X + Y will you the rates and setting p/4 + p/5 you can solve what p is equal to.

Richard0715 · Answer

I dont understand why A is not sufficient. If tom earns 80% of what Jim makes, then i get the equation .8x(5)=x(4) where I got x=6.25 plug that back into the givens and I get the answer for J. I understand how you can say that this is not giving us new information but when you plug it back in you get an answer for J.

Here was my math

.8x(5)=x(4)

5=.2x(4)
1.25=.2x
x=6.25

Can someone help me understand where I went off into the wrong direction? Ive got this problem wrong 3x in the course of my studies and cannot understand where I am losing it. Thanks

mau5 · Answer

Jim earns 4*x dollars in 4 hours = price of the jacket = 4x. 
Similarly, Tom earns 5*y dollars in 5 hours = price of the same jacket = 5y.
Thus as 4x = 5y, we have y = 0.8x

Now from F.S 1, we know that Tom makes 80% of what Jim earns  per hour --> Thus, y = 0.8x. This is exactly what we had, without the aid of any Fact Statements. Thus Insufficient.

mathivanan · Answer

Jim x dollars 4 hours 
Tom y dollars 5 hours
Since 4x = 5y, x/y 5/4; it implies y is 20% less than x
Therefore, statement (1) is redundant.

state(2)
x+y =43.75
4x=5y
therefore, x and y can be found
It is sufficient to answer the question

TaN1213 · Answer

Hello Bunuel,

Everything is fine with this question and its solution presented above, except for the part which reads- "it will take him 4 hours to earn exactly enough money to purchase a particular jacket".
Shouldn't this convert to 4x is  greater than or equal  to the price of the jacket, in compatibility with "exactly  enough  money"?
 Need your guidance here.
Thank you

Bunuel · Answer

I'd translate "enough" as  \geq  but "EXACTLY enough" as  = .

GMATGuruNY · Answer

The posted problem is the virtually the same as the following:

Distance from A to B = (Jim's rate)(Jim's time) = (x)(4) = 4x.
If we know the value of x, we can calculate the distance between A and B.
Question stem, rephrased:
What is the value of x?

Time and rate have a RECIPROCAL RELATIONSHIP.
Since the time ratio for Jim and Tom = 4:5, the rate ratio for Jim and Tom = 5:4.
Thus:
 \frac{x}{y} = \frac{5}{4}

Statement 1: 
This information is given in the prompt:
 \frac{x}{y} = \frac{5}{4}  -->  \frac{y}{x} = \frac{4}{5}  -->  y = \frac{4}{5}x = y  is 80% of x --> y is 20% less than x
Since Statement 1 offers no new information, INSUFFICIENT.

Statement 2: 
Since we have two variables (x and y) and two distinct linear equations (x/y = 5/4 and x+y=45), we can solve for the two variables.
SUFFICIENT.

B

Aatman · Answer

My doubt is that does saying 'enough' money to buy the jacket invariably say that they earned the exact amount as the jacket's cost? Could it also mean that since they are being paid per hour, after working for 4 and 5 hrs respectively, both could also earn a little more than the jacket's price? If we take this conclusion, then we cannot arrive at the exact price given the statements.

Elite097 · Answer

GMATGuruNY Bunuel KarishmaB IanStewart it says "enough" for Tom so how do we know that his pay = pay of the other person = jacket cost? Since it is enough it implies Tom's pay>=Jim's pay=jacket cost

For jim, it is clear since they mention 'exactly enough' hence his pay = jacket cost

For jim, it is clear since they mention 'exactly enough' hence his pay = jacket cost

KarishmaB · Answer

Meaning-wise, both are equivalent.
Jim ... it will take him 4 hours to earn exactly enough money to purchase a particular jacket.
Tom ...it will take him exactly 5 hours to earn enough money to purchase the same jacket.

Jim takes 4 hrs to earn  exactly enough  money to purchase. Tom takes  exactly 5 hrs  to earn enough money to purchase. So when less than 5 hrs have passed, he has not earned enough money. When exactly 5 hrs have passed, he has earned enough money which means that the money earned is the exact amount he needs.

Elite097 · Answer

KarishmaB  thanks although i do not quite see how we can confidently say that if he has worked for <5 hours, say 4.8 hours, then he has not earned enough. At exact 5 hours, he has definitely earned enough (100 rs) and jacket costs say 80 rs , but that doesnt rule out the case that at 4.9 hours he hasnt earned enough (99 rs). I have just taken random numbers to present my case although i know we d use proportionality rule to calculate this. Main point is that he could have earned enough even at <5 hours. We just dont know that and hence we dont know if he has earned  exactly enough  or not

KarishmaB · Answer

You are missing the "exactly" before "5 hrs". 
If I say you will need exactly 10 mins to complete this work, does it mean you can do it in 9.9 mins too? No. I said you will need EXACTLY 10 mins. 
So if we are given that he needs exactly 5 hrs to earn enough money, it means that he did not earn enough money in 4.99999 hrs.

Elite097 · Answer

KarishmaB  i get that but if we really think about it, your example says 'complete'. if i say i need exactly 10 mins to complete enough work, then it doesnt rule out the possibility that at 9.99 mins too i can complete enough work because lets say, the minimum time required in this case is 8 mins so any time >8 will also be enough

KarishmaB  thanks although i do not quite see how we can confidently say that if he has worked for <5 hours, say 4.8 hours, then he has not earned enough. At exact 5 hours, he has definitely earned enough (100 rs) and jacket costs say 80 rs , but that doesnt rule out the case that at 4.9 hours he hasnt earned enough (99 rs). I have just taken random numbers to present my case although i know we d use proportionality rule to calculate this. Main point is that he could have earned enough even at <5 hours. We just dont know that and hence we dont know if he has earned  exactly enough  or not

If Jim earns x dollars per hour, it will take him 4 hours to

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