Let the balance on May 1 be \(x\), on May 30 \(y\) and increase \(p\) percent.

So \(x*(1+\frac{p}{100})=y\). Question: \(y=?\)

(1) \(x*(1+\frac{12}{100})=504\) --> we can find \(x\), but still not sufficient to get \(y\).
(2) \(p=8\). Clearly insufficient.

(1)+(2) We know both \(x\) and \(p\) so we can calculate \(y\). Sufficient.

Answer: C.
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The question states : "If, during this period of time ....... would have been $504"

Note that this statement doesn't give us the actual balance amount. It just gives a condition based on the initial value.

For eg, I get a raise in salary, and you want to know my final salary.I tell you that if I had a 20% increase on my salary, it would amount to 120. Thus, you can easily guess that my initial salary = 100. But, do you know the final raise that I got? No.
Now, along with the above information, If also tell you that I DID get a 10% hike, you would be able to guess that my final salary = 110.

Similar analogy for the above problem.

Hope this helped.
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Hi,

Could you please help me here, Already answer is available in option A so why we have to rule out?

Hi All,

We're told that from May 1 to May 30 in the same year, the balance in a checking account increased. We're asked for the balance in the checking account on May 30. This question is a great example of a 'concept' question, meaning that you don't have to do any actual math to solve it (as long as you recognize the concepts involved).

1) If, during this period of time, the increase in the balance in the checking account had been 12 percent, then the balance in the account on May 30 would have been $504

Fact 1 gives us a 'hypothetical' situation, that allows us to create the following equation:
(1.12)(May 1st balance) = $504

We can use this information to figure out the initial balance on May 1st, but since we don't know that ACTUAL increase in the balance of the account, we cannot determine the total in the account on May 30th.
Fact 1 is INSUFFICIENT

2) During this period of time, the increase in the balance in the checking account was 8 percent.

Fact 2 gives us the (percent) increase in the balance of the account, but we still don't know the ending balance on May 30th.
Fact 2 is INSUFFICIENT

Combined, we know:
-The balance on May 1st
-The balance increased by 8% from May 1st to May 30th

With this information, we CAN calculate the balance on May 30th (but we don't actually have to do any of the individual math 'steps' to know that).

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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The only point that is crucial to get this Question right is that [ IF ] in Statement 1, 504 is not the balance at may 30 but it would be the balance if A certain amount X is increased at 12 % .

We use Statment 1 to get Amount X But we do not have the actual increase in amount, it is insufficient
We use Statement 2 to apply the actual increment We have the actual increase but not the amount, it is insufficient

Hence we have to use Both statements , therefore answer is C.

I understand we don't need to calculate the actual amount, but how do we know it is Compound Interest and not simple interest?

Hi jimar,

This prompt is NOT an "interest rate" question - and you probably noticed that an interest rate was NEVER mentioned. The prompt tells us that the balance simply increased - and in the context of what we are given, that means that someone deposited more money into it.

GMAT assassins aren't born, they're made,
Rich
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Bunuel
how do u know it is Compund interest and not si
also how do u we know the compunding frequency ,it may be compunded daily

Whether the account pays simple or compound interest is irrelevant. 12% in (1) and 8% in (2) are total percent increases. For example, (2) says that the increase in the balance in the checking account was 8 percent. So, if the initial balance was $100, then the end balance was $108, and it does not matter if it was simple interest of 8% per that period or compound interest, compounded 30 times, which resulted in final interest of 8%.

Hope it's clear.
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Bunuel

Can you please help me to solve the below equations quickly?

1. x= 504/1.12
2. y= 1.08*x (x calculated in step 1)

Is there a shortcut to calculate within seconds, the value of x and y.

Hi Shilpa04,

Neither of those calculations is actually required to answer this DS question, so you have to be careful about performing 'extra' math steps when you don't have to (since that can impact your overall pacing).

We're told that from May 1 to May 30 in the same year, the balance in a checking account increased. We're asked for the balance in the checking account on May 30. This question is a great example of a 'concept' question, meaning that you don't have to do any actual math to solve it (as long as you recognize the concepts involved).

1) If, during this period of time, the increase in the balance in the checking account had been 12 percent, then the balance in the account on May 30 would have been $504

Fact 1 gives us a 'hypothetical' situation, that allows us to create the following equation:
(1.12)(May 1st balance) = $504

We can use this information to figure out the initial balance on May 1st (it would be a number that we COULD calculate), but since we don't know that ACTUAL increase in the balance of the account, we cannot determine the total in the account on May 30th.
Fact 1 is INSUFFICIENT

2) During this period of time, the increase in the balance in the checking account was 8 percent.

Fact 2 gives us the (percent) increase in the balance of the account, but we still don't know the ending balance on May 30th.
Fact 2 is INSUFFICIENT

Combined, we know:
-The balance on May 1st
-The balance increased by 8% from May 1st to May 30th

With this information, we CAN calculate the balance on May 30th (but we don't actually have to do any of the individual math 'steps' to know that).

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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The principal amount on First May 1 = X, Balance on May 30 = 1.RX [R is the rate of interest]

(1) 1.12x = 504 [if the interest rate would 12% but it was 12%] Insufficient.

(2) The real interest rate was 8%, So, the balance will be 1.08x. We don't know the principal amount,i.e., the value of x. Insufficient.

Using both options:
We will get the principal amount from option (1) 1.12x = 504, which will be $450
Now applying real interest rate with the principal amount = 450*1.08 = $486

Ans. C

I know I don't need do all these calculations.
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For one : (504×100)/112=450, I don't think we have any other shortcuts. If you get let me know.
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Solution:

Question Stem Analysis:

We need to determine the balance in the checking account on May 30.

Statement One Alone:

We see that the beginning balance (i.e., the balance on May 1) of the checking account was 504/1.12 = $450. However, since we don’t know the actual percent increase in the balance, we can’t determine the balance in the account on May 30.

Statement Two Alone:

Since we don’t know the balance of the checking account on May 1, even if we know the percent increase in the account, we can’t determine the balance in the account on May 30.

Statements One and Two Together:

Since we know both the beginning balance of the checking account ($450) and the percent increase during the month (8%), we can determine the balance of the account on May 30 to be 450 x 1.08 = $486. Both statements together are sufficient.

Answer: C

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Answer: Option C

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