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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?
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Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
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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?
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Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
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Re: Jorge's bank statement showed a balance that was $0.54 great [#permalink]
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