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

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

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?

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 .....)

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-------

[ 10z + 1y ] - [ 10y + 1z ] = 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-

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

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

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).

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?

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)

­
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

Reigniting this problem: KarishmaB Bunuel gmatophobia BrentGMATPrepNow

Please someone let me know what this type of problem is called. Where can I find a robust set of practice problems similar to this one?

Thank you!

x.zy-x.yz=0.54, hence 0.(zy-yz)=0.54
let's multiply both sides by 100
=> 10z+y-(10y+z)=54
9z-9y=54
z-y=6
z and y can take values 6-0, 7-1, 8-2, 9-3..... respectively
z is the bigger of the 2 integers here ...only value from the answer options z can take is 6

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: 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!