Did the sum of the prices of three shirts exceed $60?

Target question: Did the sum of the prices of three shirts exceed $60?

Statement 1: The price of the most expensive of the shirts exceeded $30
This statement doesn't FEEL sufficient, so I'll TEST some values.
Case a: the shirt prices are $31, $32 and $33, in which case the sum of the 3 prices EXCEEDS $60
Case b: the shirt prices are $11, $12 and $33, in which case the sum of the 3 prices DOES NOT exceed $60
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The price of the least expensive of the shirts exceeded $20
If the least expensive shirt costs 20+ dollars, then the other 2 shirts also cost 20+ dollars each
(20+ dollars) + (20+ dollars) + (20+ dollars) = 60+ dollars
So, we can conclude that the sum of the 3 prices EXCEEDS $60
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Video solution from Quant Reasoning:
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Did the sum of the prices of three shirts exceed $60?

(1) The price of the most expensive of the shirts exceeded $30.
(2) The price of the least expensive of the shirts exceeded $20.

B

1) If the most expensive shirt exceeds $30, then lets say the most expensive shirt is $31. Then the two lesser shirts can cost $30 a piece. This will bring the total over $60. But the two lesser shirts can also be $5 a piece, bringing the total under $60. Not Sufficient.
2) If the least expensive shirt exceeds $20, then lets say the least expensive shirt is $21. Then the two more expensive shirts can cost $22. This will bring the total over $60. The price of the two more expensive shirts can only go up making the sum of the three over $60. Sufficient.

What if all shirts cost $20 each, then the answer can be C?
or it has to be the price of the least expensive shirt cost $20 and other shirts above $20?

Hi Zxcvbnmas,

The Question says :

Did the sum of the prices of three shirts exceed $60?

(1) The price of the most expensive of the shirts exceeded $30.
(2) The price of the least expensive of the shirts exceeded $20.

Using option (2) , we know the cost of least exp shirt exceeded 20 , which means they can be 20.01 too , Even if all the 3 costed the same , the total cost will be greater than 60

Kudos if it helped

if all three shirts cost $20, so 20+20+20=$60
60 cannot be greater than 60!
Where am I going wrong??

But how can we assume the cost to be 20 for 1 shirt , It is not mentioned in the premise

The question is asking whether the cost is greater than $60.
stmt (1) is clearly insufficient
stmt (2) the lowest value is $20
if all three shirts cost 20 each then the total value will be equal to 60
if not all three shirts equal to 20 then the total value will be greater than 60.
My question is can we assume that the least value and other two values are the same even though the statement 2 specifically stated the word "least"?
thanks in advance!

2) The price of the least expensive of the shirts exceeded $20.

The question doesn't mention the cost to be 20 anywhere , how are you deducing the cost to be 20 from the 2nd statement ?

Oh my god, I was reading stmt2 wrong, I though it was stating the lowest value is equal to $20
Thanks dude!!

(1) The price of the most expensive of the shirts exceeded $30.
what if other two shirts are only $1 each.

Then total price will be 30+1+1= 32
Not sufficient.

(2) The price of the least expensive of the shirts exceeded $20.

Least expensive shirt is >20
that means other two shirts will be >20

total > 20+20+20
>60

B is the answer
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1) Max is 30. So, total can be 30+29+28(more than 60) or 30+1+2(less than 60)

2) Least expensive is more than 20. So, total will be more than 60 in all possible cases

So, B

Sent from my Nexus 5 using GMAT Club Forum mobile app

We must determine whether the price of 3 shirts exceeded $60.

Statement One Alone:

The price of the most expensive of the shirts exceeded $30.

Without knowing the price of at least one of the other two shirts, we do not have enough information to answer the question. For example, the most expensive shirt could be $31 and the two less-expensive shirts could be $1 each, and thus the price of the 3 shirts would be less than $60. However, the most expensive shirt could be $50 and the two less-expensive shirts could be $10 each; then, the total price would exceed $60.

Statement Two Alone:

The price of the least expensive of the shirts exceeded $20.

We have enough information to determine that the price of the three shirts exceeded $60. We know that price of the least expensive shirt is greater than $20, and furthermore we know that the price of any one of the other two shirts has to be greater than the least expensive shirt. Thus, no matter what the prices of the three shirts are, the sum will always be greater than $60. Statement two is sufficient to answer the question.

Answer: B
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Nicely explained Brent.! I love your explanations and the way you always enlighten with some valuable complimentary videos or articles.
And thanks for sharing the link to your article that was really informative and helpful.

Let's talk strategy here. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full “GMAT Jujitsu” for this question:

Many people spend too much time on Data Sufficiency questions because they think they need to get to the bitter end. The question asks “Did the sum of the prices of three shirts exceed $60?” This is a “Yes/No” question – a very common structure for Data Sufficiency problems. The fundamental trap for problems like these is to bait you into thinking that you actually need to solve for every value. You don’t. As soon as you have enough information to conclude that a statement is either sufficient or insufficient, you can move on. For “Yes/No” questions, if you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. In my classes, I call this strategy “Play Both Sides.”

Let’s analyze each statement, and you will see what I mean. Statement #1 tells us that the “price of the most expensive of the shirts exceeded \($30\).” Trying to “mathematize” this into a formula is unnecessary. We just need to think of two situations that would give us different answers to the “Yes/No” question. Given the information in Statement #1, is it possible that the prices of the three shirts exceeds \($60\)? Sure. If the most expensive shirt exceeded \($30\), it is easily possible that that shirt was over \($60\) by itself. We can answer “Yes”. Is it possible the three shirts didn’t exceed \($60\)? Sure. If the most expensive shirt was \($31\), and the other shirts were free, they would sum to well less than \($60\). Since we can answer both “Yes” and “No”, Statement #1 is insufficient.

Statement #2 tells us that the “price of the least expensive of the shirts exceeded $20.” The primary bait behind this statement is to trick you into turning your brain off. Statement #2 is very similar in appearance to Statement #1. It sounds like it is playing the same game. But when you see similar statements in Data Sufficiency questions, you should start by looking at how the statements are different, and see if those differences are meaningful. You see, if the “least expensive” shirt exceeded \($20\), then we can’t get any free shirts. Every shirt must cost more than \($20\). And since the problem tells us that we are buying “three shirts”, then the total cost must be greater than \(3*($20)\). The price must exceed \($60\). Statement #2 is totally sufficient.

The answer is “B”.

Now, let’s look back at this problem through the lens of strategy. This question can teach us patterns seen throughout the GMAT. First, notice that this problem is much more about logic and critical-thinking than it is about math. With “Yes/No” questions, a great tactic that you can often use is to plug in easy, hypothetical values that provide different answers to the question. Naturally, those values must follow the constraints inside the question, but if you can do this, you can “Play Both Sides” and disprove sufficiency. Second, similar-looking statements in Data Sufficiency questions often bait you into thinking that you must solve each statement in the exact same way. The trick is to leverage the differences between the statements, rather than thinking linearly and assuming because they sound the same that they play the same game. And that is how you think like the GMAT.

Answer: Option B

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