Last visit was: 17 Jun 2024, 05:53 It is currently 17 Jun 2024, 05:53

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 28944
Own Kudos [?]: 33719 [25]
Given Kudos: 25363
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11807 [15]
Given Kudos: 136
Send PM
General Discussion
Verbal Expert
Joined: 18 Apr 2015
Posts: 28944
Own Kudos [?]: 33719 [2]
Given Kudos: 25363
Send PM
avatar
Intern
Intern
Joined: 06 Jan 2022
Posts: 6
Own Kudos [?]: 3 [2]
Given Kudos: 0
Send PM
Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
2
GreenlightTestPrep wrote:
Carcass wrote:
Jorge's bank statement showed a balance that was $0.54 greater than what his records showed. He discovered that he had written a check for $x.yz and had recorded it as $x.zy, where each of x, y, and z represents a digit from 0 though 9. Which of the following could be the value of z ?

A. 2
B. 3
C. 4
D. 5
E. 6



Key concept: a.bc \(= a + b(\frac{1}{10}) + c(\frac{1}{100})\)
For example: \(3.25 = 3 + 2(\frac{1}{10}) + 5(\frac{1}{100})=3+0.2+0.05=3.25\)

Jorge wrote a check for $x.yz BUT recorded it as $x.zy. His bank statement showed a balance that was $0.54 greater than what his records showed
This tells us that: $x.zy - $x.yz = 0.54
Now apply the above concept to write: \([x + z(\frac{1}{10}) + y(\frac{1}{100})]-[x + y(\frac{1}{10}) + z(\frac{1}{100})]= 0.54\)

Subtract \(x\) from both sides to get: \([z(\frac{1}{10}) + y(\frac{1}{100})]- [y(\frac{1}{10}) + z(\frac{1}{100})]= 0.54\)

Multiply both sides by \(100\) to get: \([10z + y]- [10y + z]= 54\)

Simplify to get: \(9z - 9y= 54\)

Divide both sides by \(9\) to get: \(z - y= 6\)

Rearrange to get: \(z = y + 6\)

Since y is a DIGIT, the possible solutions are
y = 0 and z = 6
y = 1 and z = 7
y = 2 and z = 8
y = 3 and z = 9
And that's it!

Since z can be 6, 7, 8 or 9, the correct answer is E

Cheers,
Brent




why not x.yz as 1.82 and x.zy as 1.28
difference is still .54?


EDIT: Shouldn't it be x.yz - x.zy = .54?

as balance = .54 + records
and its given that he recorded it as x.zy?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11807 [2]
Given Kudos: 136
Send PM
Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
2
ChandanPednekar wrote:
GreenlightTestPrep wrote:
Carcass wrote:
Jorge's bank statement showed a balance that was $0.54 greater than what his records showed. He discovered that he had written a check for $x.yz and had recorded it as $x.zy, where each of x, y, and z represents a digit from 0 though 9. Which of the following could be the value of z ?

A. 2
B. 3
C. 4
D. 5
E. 6



Key concept: a.bc \(= a + b(\frac{1}{10}) + c(\frac{1}{100})\)
For example: \(3.25 = 3 + 2(\frac{1}{10}) + 5(\frac{1}{100})=3+0.2+0.05=3.25\)

Jorge wrote a check for $x.yz BUT recorded it as $x.zy. His bank statement showed a balance that was $0.54 greater than what his records showed
This tells us that: $x.zy - $x.yz = 0.54
Now apply the above concept to write: \([x + z(\frac{1}{10}) + y(\frac{1}{100})]-[x + y(\frac{1}{10}) + z(\frac{1}{100})]= 0.54\)

Subtract \(x\) from both sides to get: \([z(\frac{1}{10}) + y(\frac{1}{100})]- [y(\frac{1}{10}) + z(\frac{1}{100})]= 0.54\)

Multiply both sides by \(100\) to get: \([10z + y]- [10y + z]= 54\)

Simplify to get: \(9z - 9y= 54\)

Divide both sides by \(9\) to get: \(z - y= 6\)

Rearrange to get: \(z = y + 6\)

Since y is a DIGIT, the possible solutions are
y = 0 and z = 6
y = 1 and z = 7
y = 2 and z = 8
y = 3 and z = 9
And that's it!

Since z can be 6, 7, 8 or 9, the correct answer is E

Cheers,
Brent





why not x.yz as 1.82 and x.zy as 1.28
difference is still .54?


EDIT: Shouldn't it be x.yz - x.zy = .54?

as balance = .54 + records
and its given that he recorded it as x.zy?


Let's look at a specific example.
Let's say that, at the beginning of the day, Jorge has $5.00 in his bank account.
He writes a check for $1.06 but accidentally records it as $1.60.
So, according to his records, Jorge THINKS the amount remaining in his account = $5.00 - $1.60 = $3.40
So, when he looks at his bank statement, he EXPECTS to see $3.40 in his account.

However, since the check was actually for $1.06, the ACTUAL amount in his account = $5.00 - $1.06 = $3.94, which is $0.54 more than he expected.

In other words, $x.zy - $x.yz = $0.54

Does that help?
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4603
Own Kudos [?]: 69 [0]
Given Kudos: 0
Send PM
Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1088 posts
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne