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Please allow me to correct your language, because using the wrong terms can often lead to making mistakes. You don't mean to ask me whether this is sufficient to "reject the statement". Rather, you are asking whether it is sufficient to "confirm that the statement is NOT sufficient to answer the question". In order to confirm that it's not sufficient, we must show that the statement allows for both a YES and a NO - and is therefore not capable of offering a definitive answer to the question. Once you've shown that statement 2 allows for x to be equal to -3, which would produce the answer NO to the question, you must also show that statement 2 allows for x to be less than -3, which would produce the answer YES to the question. You could show that (-3)^3 = -27 and (-4)^3 = -64, and therefore x could be either -3 or -4. Those values of x produce differing answers to the question. Now we can confidently eliminate answer choices B and D.

Yes, and kind of yes. We reduced the ratio of the times by their greatest common factor to take advantage of the integer constraint. We wouldn't be using "the times as originally provided", because the question isn't asking about "time". But the numbers would match the times as originally provided - only because the original greatest common factor happened to be 2, just as in your hypothetical question.

I didn't fully understand the explanation on the second question, could you assist me? So, if we were asking how many laps would Candice completed the 3rd time they were together we would calculate d= r*t = (23/21)*3 = (23/3*7)*3 = 23/7 = 3.2 and we would round to 3?

No, a non-integer answer (in this case 3.2) doesn't make any sense. Remember, the original question was "How many laps around the track had Candice completed the next time that Candice and Sabrina were together *at the starting point*?" So if your approach leads you to a non-integer, that's a clue that there's something wrong with your approach. I use the 21/23 fraction only in order to compare the speeds, e.g. Sabrina is 21/23 as fast as Candice. I'm not sure how you came up with the equation d= r*t = (23/21)*3 as I don't believe 23/21 represents the rate of anything, nor does 3 represent time. Is it 3 seconds? 3 minutes? No, you're using 3 because you want Sabrina and Candice to have met at the starting point 3 times. That is not a measurement of time. Sabrina will meet Candice at the starting point every time Sabrina completes 21 laps - and Candice will have completed 23 laps each of those times. Please rewatch the video and let me know if you're still confused about this.

Thank you Avi!! I understand the complete picture, and it's crystal clear to me what my mistake was and how to handle questions like this.

Looks good to me.

S is not less than 5/4

Right, my bad! I thought that I could restrict it between the first and last term but I just added them an it's 1,54

Yeah, S is a sum of all those numbers, so if the first two numbers give us 5/4, and then we're adding more positive numbers, S will be greater than 5/4.

Because that's the cycle length of the units digit's repeating pattern. Here's an analogous scenario: Today is Monday. What day will it be 100 days from now? Well, 100/7 has a remainder of 2, so the answer is Wednesday (2 days after Monday). Why did I divide by 7? Because that's the cycle length of the repeating pattern of days of the week.

Correct

Yes.

Not quite. Two equations with two unknowns are guaranteed to be solvable if those equations are LINEAR and DISTINCT. Simplifying your equation, you get 20*◼︎ + 30*▲ + ◼︎*▲ = 264 That’s not a linear equation, because of the product ◼︎*▲. Likewise, statement 2 is not a linear equation. The reason the answer is D is that we have constraints on the possible values of ◼︎ and ▲, namely that they are both single digit integers.

If k=0, then 10^k = 1. Then the value of the expression is a fraction, but we were told that it’s an integer.

@@QuantReasoning Thanks Avi. very helpful

Nothing would happen. Divisibility questions are always limited to positive integers, because there's no point in bringing in the mirror image on the left side of zero.

@@QuantReasoning thanks a lot.

That case I invented was for statement 2, not statement 1.

This part is correct: (m + p)^2 / 2 - 50 < mp From there, it seems to me that in order to get to your next step, you treated the inequality as if it were an equation: (m + p)^2 / 2 - 50 = mp (this is NOT true) Here you can say that since we know mp is positive, we can infer that (m + p)^2 / 2 > 50 But, you're relying on a false equation.

I'm not sure I follow your question, but please note that all four factors (12, 14, 24, and 28) appear in the answer choices. So we do have to apply some reasoning and be very careful with what exactly the question is asking for. It's asking for the estimated number of hours.

@QuantReasoning I know that all factors are in the choices, I just considered that maybe in the specific factoring of 336 (in 2:41) the 2 numbers which are the estimated of A,E and the actual of B, is some kind of hint. But apparently it is pure coincidence.

At the moment it’s online only, $20/month There’s also a link in the website for folks who can’t afford the monthly subscription

What do you think would be the impact of such info?

@@QuantReasoning In that case we will be able to calculate the max score as we have the interval & the mean & we know that the data points will move by 5 on each step above or below the mean.

@@akhilkapoor413 Here are two symmetrical sets of 10 terms with a mean of 75 and a standard deviation of 5: 64, 73, 75, 75, 75, 75, 75, 75, 77, 86 65, 70, 75, 75, 75, 75, 75, 75, 80, 85 First set leads to an answer of 86, second set leads to an answer of 85. Therefore, the correct answer is still (E).

If this is in reference to PS136 from OG2018, the question isn't about divisibility by 2 (odd/even), but rather about divisibility by 3. And, n and n-4 are not of the same "type" in the context of divisibility by 3.

i got it sir.

In MSR I take a quick look at the kind of info available to me, then read the question and hunt for the required details for that particular question. Most of the information provided isn't necessary, so in that sense it's similar to RC detail questions.

@@QuantReasoning Thank you Sir

You should always use common sense when studying the "rules" of algebra. For example, why would the sign flip if we triple two sides of an inequality? Surely, the side that is farther to the right on the number line will STILL be farther to the right once we've tripled the sides. 4﹥1 and 12﹥3, for example. It's only when we multiply an inequality by a negative number that we must flip the sign, and this is because the negative factor transforms the story across zero to the other side of the number line, where everything is the mirror image. For example, 4﹥1 but -12﹤-3.

@@QuantReasoning That makes sense. Thanks

Excellent!

Ehm I think I just answered my own question haha, because -10^20 < 0 lol right? so it's not the least possible product

Right!

Yes, that’s exactly right. The closer the average is to one side, the heavier weighted that side is. Similar to the game ‘tug of war’.

Looks like a coincidence to me. What does t represent in your calculation?

It represents the time in which Ben left SD. So as to build a relationship between their time of leaving. Having only one unknown we can find at what time the dispatcher retrieved the data.

I'm confused by this. If t is the time at which Ben left SD, then t = 8:00AM. And you're trying to solve for t? I don't get it.

Because Al left SD 3 hours after Ben, I used Ben as a reference point with the variable t to see based on the total distance they both traveled (d=240m) and their speed (r1=40mph and r2=20mph) what time it was when the dispatcher collected the data ("At a particular time" as it says the stem)

So it sounds like you defined t as "the number of hours that Ben traveled". Then it follows that Al traveled (t-3) hours. Now you can express the total distance traveled as: 20t + 40(t-3) = 240 60t - 120 = 240 60t = 360 t = 6 So 6 hours after 8AM is 2PM. But I don't think that's what you did...

Knowing the average height of class X (120cm) and knowing the combined average height of both classes (126cm) does not allow you to infer the average height of class Y, because we don't know the ratio of the class sizes. For instance: if each class has the same number of students, it follows that the average height of class Y is 132cm, whereas if class Y has twice as many students as class X, it follows that the average height of class Y is 129cm.

Oh okay, I thought about it just as being variations (for instance x the average of class x and y the average of class Y) and that we were looking for x/y. So we could find Y through the sum, but now I understood my mistake. How would the question stem and statements should be written so as to use the reasoning I mentioned before?

You mean this reasoning: "we can plug in the value of average class X from the first statement and so we will find the average class Y" Well, it seems that you were thinking: if I know the sum of two numbers, and I know one of those numbers, then I can infer the other number For instance, if a + b = 7, and a = 3, then I can infer that b = 4. Is that the reasoning you used? That works for a sum of two numbers... But our word problem is dealing with a weighted average of two numbers, not a sum of two numbers. A weighted average of two numbers depends on the ratio of those weights, so that's another dimension we have to consider...

Exactly! That's what I was thinking Avi. So essentially we have 4 variables (the number of students in both classes and the sum of the heights of each class). So, even if there was another wording of the question stem and statements, I couldn't use this reasoning, am I correct?

It's a bit dangerous on the GMAT to view things in terms of number of variables, especially on DS. Here, for example, it would be correct to say that there are only 3 variables: average height of class X, average height of class Y, and ratio of class sizes (e.g. number of students in class X : number of students in class Y). To answer your question: "even if there was another wording of the question stem and statements, I couldn't use this reasoning, am I correct?" That's a hard question to answer, because it's extremely vague. I mean, what dose "another wording" mean? Another wording could turn it into a much simpler question, such as my earlier example of (a + b).

I think you’re asking whether a word problem on the GMAT might try to trick us by making us incorrectly assume that no other changes were made. I have never seen a GMAT problem do that. The language here gives us no reason to believe that any members might have joined or left a committee mid-year.

The second half of answer choice C is correct... If one of the statements is sufficient on its own, then of course both statements together are sufficient, right? In fact, the second half of answer choice C is correct 80% of the time (the only time it's wrong is when E is the correct answer). So your mistake was in eliminating B. It seems that you might have been too quick to decide that statement 2 is NOT sufficient on its own.

That’s great reasoning! But, E also satisfies the condition.

​ @QuantReasoning thank you! 🙂 That's right, so we'll focus on these two and denoting the employees in 2000 as x0, in 2003 as x3, in 2006 as x6, we can say that x3 = (5*x0)/4 and x6 = (2*x3/3). Then we substitute x6 = 100 and we find that x0 = 120. Am I correct?

@@linatavanidouLooks good!

@@QuantReasoning Great thanks! Also, congrats for your videos, whenever I'm confused for a question, I'm looking it up to your channel.

Because 1 isn't one of the options in the answer choices.

Yes, this is an official GMAT problem

You can choose whichever number is convenient for this method. It will work regardless of which number you pick.

Because that's what the question was asking for.

To find the value of (x+y)/3, we first need to find the values of x and y. We can solve the given system of equations using elimination: * Multiply the first equation by -2: -4x - 2y = -14 * Add the second equation: -3x = -9 * Divide by -3: x = 3 Now substitute x = 3 into the first equation: 2(3) + y = 7 6 + y = 7 y = 1 Finally, calculate (x+y)/3: (3+1)/3 = 4/3 Therefore, (x+y)/3 = 4/3.