12 Days of Christmas GMAT Competition - Day 9: If Mary's balance

yes/no type DS question.

Consider St 1) highest closing balance in the account was 3 times the lowest closing balance.
We are already given that one of the balance = $1400, So the highest balance must be >=1400.

lets check lowest balance at 1400 will be 1400/3 = 466.66

Hence the lowest balance is >= 466.66
i.e. lowest balance would atleast be 466 which is clearly > 450
i..e at any day the balance would atleast be 450. SUFFICIENT

St 2) i have no information about the lowest balance. NOT SUFFICIENT

Answer is option A

We need to see if the net amount withdrawn is less than 950

Statement 1: Highest closing balance will be atleast 1400, if some amount is added later

Let lowest balance be x

1400>= 3x
x<= 466 (approx)

If this is the lowest, there was no other day when the amount was less than this. So this statement is Sufficient

Statement 2: This statement alone doesn't give enough information to know weather the closing balance in the account at least $450 on each day. Insufficient

Answer A

1) Let's test extremes

Assume that $1400 was the lowest closing balance. Hence in that case we know that the closing balance in the account at least $450 on each day of January 2025.

Assume that $1400 was the highest closing balance. In that case, the lowest closing balance was, $1400/3 , ~ $466. Hence in that case we know that the closing balance in the account at least $450 on each day of January 2025.

This statement is sufficient.

2) We know that the highest closing balance was $1500. However, we don't know what the lowest closing balance is. Hence, this statement alone is not sufficient.

Option A

Closing acc balance on Jan 1 = $1400. Was the closing balance each day >= $450?

Statement 1 - Highest closing balance = 3*Lowest closing balance

We know $1400 was the closing balance on Jan 1, let's assume this is the highest balance. That means min closing balance = 1400/3 = $466 which helps us answer the question with Yes. Hence, it's sufficient.

Note - Even if $1400 is not the highest balance, any other value greater than $1400 will always lead to min balance > $466, so this should hold true for all cases.

Statement 2 - Highest closing balance = $1500
No other information on lowest balance is stated, hence insufficient.

Answer: A

Stmt (1) During January 2025, the highest closing balance in the account was 3 times the lowest closing balance.

Let's assume the highest is H. We know that H>=1400.

We also know that H=3L. So 3L>=1400.

L>=466.66. >450. Hence stmt 1 alone is sufficient.

Stmt (2) The highest closing balance in the account during January 2025 was $1,500.

But we don't have idea on the lowest it can be 300 or 500 or 1400. Not certain. Hence insufficient.

Hence IMO A

Statement 1

We know that on 1st Jan, Mary's closing balance was $1,400. Therefore, the highest closing balance can be $1,400 or more.
Now, if the highest closing balance = $1,400, then the lowest closing balance = 1400/3 = approx. $467 which is more than $450. SUFFICIENT

Statement 2

The lowest closing balance could be less or more than $450 on one of the days of Jan. INSUFFICIENT

Answer A.

On analyzing statement 1,

During January 2025, the highest closing balance in the account was 3 times the lowest closing balance.

If we assume 1400 dollars to be the highest closing balance in January then the lowest closing balance would be 1400/3=466.66 dollars which is sufficiently more than 450 dollars.

But remember that this is assuming that 1400 is the highest value in January. 1400 is the lowest possible value of the closing balance in January & there are higher possible values than 1400 for which the lowest closing balance would always be over 450 dollars

Hence (A) is sufficient & we can eliminate options (B),(C) &(E).

On analyzing statement 2,

The highest closing balance in the account during January 2025 was $1,500.

This is insufficient on its own to answer the question as we do not know its relation to the lowest closing balance. hnece statement 2 is insufficient & we can eliminate option (D)

Hence the correct answer is option (A) During January 2025, the highest closing balance in the account was 3 times the lowest closing balance.

Statement (1):
During January 2025, the highest closing balance in the account was 3 times the lowest closing balance.
Let the highest balance be H and the lowest balance be L. According to this statement:
H=3L
We know that the closing balance on January 1, 2025, was $1,400. Thus, H≥1,400 because 1,400 must fall between L and H. Since H=3L:
L=H/3
If H≥1,400, then:
L=H/3≥(1,400/3)≈466.67
Thus, the lowest possible balance during January 2025 was at least $466.67, which is greater than $450. Therefore, the closing balance was at least $450 on each day.
Statement (1) alone is sufficient.

Statement (2):
The highest closing balance in the account during January 2025 was $1,500.
This provides H=1,500, but it does not establish any direct relationship between H and L. For example:

• If the lowest balance L was $300, the balance would not meet the requirement of being at least $450 every day.
• If L was $600, the requirement would be satisfied.

Since we cannot determine the lowest balance L from this statement, it is insufficient.

1. Even if we consider 1400 was the highest amount ever reached, then lowest = 1400/3 = 466.67
Thus the amount always remains>=466.67, i.e. higher than 450..... SUFFICIENT.

2. any day balance can be 1500 or 1400 or 250. This doesn't give any data.. NOT SUFFICIENT

Answer A

If Mary's closing balance in a bank account was $1,400 on January 1, 2025, was the closing balance in the account at least $450 on each day of January 2025?


(1) During January 2025, the highest closing balance in the account was 3 times the lowest closing balance.

say, $ 1400 (on January 1 2025) be the highest closing balance (for January 2025).

then, the lowest closing balance = 1400/ 3 = $ 466 2/3 > $ 450

If the highest closing balance be any amount higher than $ 1400, it still means that the closing balance was higher than $ 450

So, YES is the answer ( i.e. the closing balance in the account at least $450 on each day of January 2025 )


SUFFICIENT


(2) The highest closing balance in the account during January 2025 was $1,500.

From the given statement, the Closing Balance on other days of January 2025 can't be determined.

INSUFFICIENT




(A) is the CORRECT answer

Let's look at the answer options:

(1) In the worst-case scenario, the highest balance was already 1,400 on January 1st. Then, the lowest could've only been ~466 dollars, which is already more than 450. If the highest balance was even larger, then we're moving only in the bigger territory. Sufficient.

(2) Knowing the highest balance gives us absolutely no view into the lowest one. Insufficient.

Thereefore, the answer is A.