Jorge's bank statement showed a balance that was $0.54 greater than wh

Question

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

PS65741.02

A. 2
B. 3
C. 4
D. 5
E. 6

PS65741.02

BrentGMATPrepNow · Accepted Answer

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:   - = 0.54

Subtract  x  from both sides to get:   -  = 0.54

Multiply both sides by  100  to get:   -  = 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

lacktutor · Answer

x.zy— x.yz = 0.54 
—> zy —yz = 54
10z+ y—10y —z = 54
9z —9y = 54 
z —y= 6 
Each of x,y and z represents a digit from 0 through 9 
—> 9 —3= 6 
—> 8 —2 = 6
—> 7 —1 = 6
—> 6 —1 = 6 
z could be 9, 8, 7 or 6

Answer ( E)

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abalodi · Answer

Can someone please explain why its arranged so that x.zy - x.yz instead of x.yz - x.zy? I understand the solution but dont understand how it makes sense that his balance is .54 greater with records being greater than check instead of check being greater than records?

itspCv2 · Answer

Ok let's make it easy for beginners: straight to point

He has 0.54 extra---> reason: he recorded 0.54 less in his records i.e., x.zy instead of x.yz >>>> (x*1+z*0.1+y*0.01) -(x*1+y*0.1+z*0.01) =0.54 multiply with hundred on both sides>>>>(10z+y)-(10y+z)=9(z-y)=54 >>>> z-y=6 >>>>z=6+y There for z can be greater than or equal to 6(6 to 9 since they are digits as given in question). Therefore answer is E.6 Hope this helps THANKS

unraveled · Answer

abalodi 
 rohansabat  brings a logical point. Let's take it and try to solve.
Assume balance before the check was written = B
Balance as per Bank after the check was written,  B_B  = B - x.yz
Jorge's Balance with the error,  B_J  = B - x.zy

Now,
 B_B - B_J  = 0.54
B - x.yz - B + x.zy = 0.54 (basically B - x.zy < B - x.yz)
0.zy - 0.yz = 0.54
9(z - y) =54
z - y = 6
z = 9, 8, 7, 6

Only 6 is in the option.
Answer E.

rajpurohitchirag  HTH.

(You may take example also: 
B - 106 - B + 160 = 54 OR
B - 128 - B + 182 = 54 .....)

Fdambro294 · Answer

His Actual Bank Balance >>> What he recorded

This means that the Check he gave to someone must be written down in his records as GREATER THAN the Actual Check that he gave away ---- only in this scenario, logically, would he have more money in his Bank Account than he originally thought that he had

His Recorded Check = X.ZY > ACTUAL Check the Bank cashed = X.YZ

The Difference between: (Recorded Check) - (Actual Check) = $.54 Greater amount

X.ZY - X.YZ = .54

.ZY - .YZ = .54

----multiply Each Side by * (100) ------

ZY - YZ = 54

-----where Z and Y are Digits from 0, 1, 2 ......9-------

-   = 54

10z - 1z + 1y - 10y = 54

9z - 9y = 54

9*(z - y) = 54

(z - y) = 6

The Difference between the Z-Digit and the Y-Digit must be Exactly = 6

therefore, the MIN Value the Z-Digit can take is = 6

only Answer Choice -E- is possible out of the Answer Choices provided

z = 6
y=0

X.ZY - X.YZ =

$10.60 - $10.06 = $.54 cents

-E-

ScottTargetTestPrep · Answer

Solution:
 
Since the bank statement has a balance that is greater than his records, the check he wrote must be less than what he had recorded. That is, x.yz < x.zy, and their difference is 0.54. Therefore, in cents, we can create the equation:

(100x + 10z + y) - (100x + 10y + z) = 54

9z - 9y = 54

z - y = 6

z = 6 + y

Since y is nonnegative, z must be at least 6. Therefore, E is the correct answer.

Answer: E

pk6969 · Answer

I have a doubt. Why are we subtracting x.yz from x.zy? I think that we should take the case of depositing because written a check could mean deposit too. If we take the case of withdrawal then only I think it should be x.zy - x.yz. this is ambiguous. Can someone please help?  BrentGMATPrepNow  @veritasprepkarishma  TargetTestPrep   Bunuel

BrentGMATPrepNow · Answer

When you "write a check" you are agreeing to transfer money from your bank account to somebody else's bank account (not the other way around).

brains · Answer

KarishmaB

The Bank showed $0.54 greater than the records kept by the consumer. So, if only it is $0.54 difference, then Z can also take the value of 3.
For example. 8.93(Bank statement)
Consumer's record: 8.39( Check)
The difference is $0.54

According to this, if bank shows $8.39 and the consumer recorded $8.93, then the bank will not clear the check. Further, It is said in the question that the Bank statement shows $0.54 more than his record. Then how come Z cannot take the value of 3?

KarishmaB · Answer

x.yz and x.zy are not the amounts on bank statement vs consumer records. They are amounts of the check vs amount of the check on consumer records. So whatever his bank balance was, $x.yz, the smaller check amount, was deducted from it but the consumer recorded it as $x.zy (a larger amount) and hence expected a lower leftover bank balance. The larger amount was $0.54 more than the smaller amount.

Since x is the same for both, zy - yz = 54
10z + y - 10y - z = 54
9(z - y) = 54
z-y = 6

So z could be 9, 8, 7 or 6.

Answer (E)

gmatophobia · Answer

x.zy - x.yz = 0.54

Multiplying by 100 on both sides

xzy - xyz = 54

100x + 10z + y - 100x - 10y - z = 54

9(z-y) = 54

z - y = 6

z = 6 + y

As y is non negative, the value of z must be greater than or equal to 6. Among the given options, only one value satisifies.

Option E

GMATGuruNY · Answer

Let x=1 and y=0, implying that the two dollar values are 1.z0 and 1.0z.
We can PLUG IN THE ANSWERS, which represent the value of z.
When the correct answer is plugged in, the difference between the greater dollar value and the smaller dollar value = 0.54

D: z=5, implying that the two dollar values are 1.50 and 1.05
In this case, the difference between the values = 1.50 - 1.05 = 0.45
Too small.
For the difference to increase to 0.54. a greater value is needed for z.

E

E: z=6, implying that the two dollar values are 1.60 and 1.06
In this case, the difference between the two valuies = 1.60 - 1.06 = 0.54
Success!

SanchitSanjay · Answer

Could someone please help me understand, numerically - if I were to take a pure raw example of 5.82 (x.yz) and 5.28 (x.zy); the difference is 0.54. Why wouldn’t this be one of the consideration?

Bunuel · Answer

Good question. But in the problem, Jorge  wrote  the check for  $x.yz  and  recorded  it as  $x.zy . In your example,  $5.82  was written and  $5.28  was recorded. This means the bank would show less money than Jorge’s record. However, the question says the bank shows  more  money by  $0.54 .

That is why your example does not work. The recorded amount must be greater than the actual check for the balance to appear higher.

findingmyself · Answer

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

PS65741.02

From a logical POV, His actual is 0.54 more than recorded, which means he recorded a higher value. Thus x.zy>x.yz and the diff between the two will be 0.54

Thus we have x.zy-x.yz=0.54---> .zy-.yz=.54 
 Multiply both sides with 100 
 zy-yz=54 
 10z+y-10y-z=54 
 9(y-z)=54 
 y-z=6 
 z=y-6 
 Only option E (6) gives z a positive value 
 Also you can substitute to double check 
 let x be 1, y=0 and z=6 
 1.60-1.06= 0.54 (BINGO:))

Wadree · Answer

He assumed he had less money but actually he had more money....... because he recorded more than he spent.... So...........record = $ x.zy > $x.yz = actual....so..... zy > yz .......now....lets take two digits 7 and 8....we wanna make 78....but how do we do that....like this ( 7×10 ) + 8 = 78..... So....zy = 10z + y.....yz = 10y + z.....now....his record and actual expenditure had $ 0.54 difference.... So 10z + y - ( 10y + z ) = 54.....so 9z - 9y = 54 ....... z - y = 6 ..... z = y + 6 
Now, y can be 0, 1, 2 and 3..... So that z can be 6, 7, 8 and 9 respectively....so da only option that matches is E or 6...

Prak0709 · Answer

Can someone explain why its records- written value even though the first statement in question states the opposite ?

Bunuel · Answer

Because the bank balance is  greater  than Jorge’s records, his records must have deducted  more  than the bank did. That happens only if the  recorded amount is larger than the written amount , so the difference is recorded minus written, not the other way around.

Jorge's bank statement showed a balance that was $0.54 greater than wh

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Jorge's bank statement showed a balance that was $0.54 greater than wh

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