High Score Questions

Question

How smart you think you are? A 800+ GMAT Question

A set of thirteen numbers has an average (arithmetic mean) equal to 3. If two numbers are removed from the set and replaced with the number 7, the new average of the set is equal to 4. What two numbers were removed from the set?

A) 1.5 and -0.5
B) -1.5 and 0.5
C) 0 and 1.0
D) -1.0 and 0
E) -1.5 and -0.5

Similar questions to follow on due course

srini123 · Answer

A or C both can be the answer in my view

sum(13 numbers with avg 3) = 39

sum (13 numbers with avg 4) = 52

difference is 52-39 = 13

so the sum of the two numbers removed is 1 , C and A meet the criteria

getmba · Answer

Sum of 13 numbers with average 3 = 39

Two numbers are removed and one number, 7, is added
Sum of 12 numbers with average 4 = 48

Difference between new and old sum = 48-39 = 9
So sum of two numbers removed will be = 7-9 = -2

Answer should be E.

shalva · Answer

I think that's the correct solution. Question stem clearly states that "number 7" was added; so now set consists of 12 numbers, not 13

srini123 · Answer

Yep, getmba and shalva seem right.

for me the question is little ambiguous..

LUGO · Answer

As set of five positive numbers has an average (arithmetic mean) equal to 3 and a standard deviation equal to the root square of 2. If two of the numbers in the set are 4 and 5, what are the other three numbers?

A) 6,7,8
B) 5,6,7
C) 2,3,4
D) 1,2,3
E) Can not be determined

A) 6,7,8
B) 5,6,7
C) 2,3,4
D) 1,2,3
E) Can not be determined

BarneyStinson · Answer

D is the answer. Plain and simple.

Set has five positive numbers, n = 5.
mean of the set, m = 3.
Sum of all elements of this set will be, n * m = 15.
Two of the numbers is given as 4 and 5. Their sum is 9. Sum of remaining numbers in the set is 6.

which implies none of remaining positive numbers in the set as defined can be greater than 6. Hence, options A and B eliminated. Sum of the three elements in option C is not 6, but D sure is.

LUGO · Answer

Good - it meant to be simple but what if among the 5 answers provided, you have three answers that add up to 6. Can you explain how you reach the solution? Although the question above was in the 500-600 range, this one now is closed to 750. Let see how well you do - Good luck!!!

BarneyStinson · Answer

This is the beauty of GMAT my friend. In fact, the essential trait of a Manager. No one demands perfection. You don't have to be excellent. All you need to do is SOME HOW quickly solve the problem at hand, and move on!!!! Eliminating answer options is the best approach. That's what even managers do to run businesses, indeed the President does to run the country, and the world. Choose what's best among those offered and it ends there.

First off, the set contains positive numbers as mentioned in the problem statement. Second, sum of two positive numbers from the set is 9 which is taking a greater proportion of the overall sum 15. So essentially, the remaining numbers have to have a lower significance over these two given numbers. Third, only option now remains is to eliminate answer choices based on the information we have. Agreed, if there were decimal numbers like 1.2 and 2.3 among the answer options, we'd have to consider the standard deviation as well, but as long as that's not the case, go with the easier option of POE to save time, energy, cost of taking the exam and emotional investments that were put into it.

Overall, there is no time to evaluate all of this stuff above for each and every problem. If you have the ability to figure out what is wrong, that is it, done then and there and just move on with the next question. There is an entirely different section on the GMAT exam to evaluate how you analyse a given problem/situation at hand, that's called the AWA.

LUGO · Answer

Question 3:
The average (arithmetic mean) of a set of five numbers is 15. If the sum of the squares of the numbers in the set is 135, what is the standard deviation of the set?

A) 0
B) sqrt (3)
C) sqrt(2)
D) 3 sqrt (2)
E) 4

srini123 · Answer

what material u followed for verbal ?

chuckberry007 · Answer

We need to find whether if the std dev is really  \sqrt{2}

Finding the std dev since we know the mean is 3

(5-3)^2=4 
 (4-3)^2=2 
 (3-3)^2=0 
 (2-3)^2=2 
 (1-3)^2=4

Total = 10 
Average = 10/5 =2 
Std dev =  \sqrt{2}

LUGO · Answer

Hi chuckberry007

The standard deviation is given. The question ask for the remaining 3 numbers in the set. Try Question 3 which uses similar approach to Question 2 but this time the question is rephrased slightly different.

Hint: Need to know the relationship between the sum of the squares and the variance of the distribution.

Let me know if you need help

Regards

LUGO · Answer

Just OG12 in order to understand the format of the questions.

IanStewart · Answer

The answer here is not D; just because the other numbers  could  be 1, 2 and 3 does not mean they  must  be 1, 2 and 3. We have a set {x, y, z, 4, 5}. We know their sum is 15, so x+y+z = 6. Further, we know the standard deviation is sqrt(2), so the variance is 2. No real GMAT question actually requires you to compute variance (or standard deviation), so the following is not important for the test, but we can use the definition of variance to get a relationship among x, y and z:

/5 = 2
x^2 - 6x + 9 + y^2 - 6y + 9 + z^2 - 6z + 9 + 1 + 4 = 10
x^2 - 6x + y^2 - 6y + z^2 - 6z + 22 = 0
x^2 + y^2 + z^2 - 6(x + y + z) + 22 = 0

and substituting x+y+z=6 we have

x^2 + y^2 + z^2 - 36 + 22 = 0
x^2 + y^2 + z^2 = 14

So we only have these two relationships among our three unknowns. In 3-d coordinate geometry, a subject well beyond the scope of the GMAT -- none of what follows is tested -- the equation x+y+z=6 defines a plane perpendicular to (1,1,1) and passing through (to take one example point) (1,2,3), while x^2 + y^2 + z^2 = 14 is a sphere centered at (0,0,0) with radius sqrt(14). Using 3-d coordinate geometry principles, you can determine that these must intersect in a circle; there is an infinite set of points (x,y,z) which satisfy these two equations. So the answer to the above question is E, not D.

LUGO · Answer

Correct! What about Q3, surely this could easily be tested in the GMAT!! I did mine but the questions were very straight forward and got an 800 :-D

IanStewart · Answer

And Lugo, the GMAT score you list under your name is impossible; one cannot score higher than a 51 in either section of the test. And since you've posted elsewhere that your score was in the 700s (you said you had a Q46/V41 breakdown), I'm not sure why you list your score as an 800?

IanStewart · Answer

The question doesn't make any sense. If the average of the five numbers is 15, one of the numbers must be at least as large as 15, and its square must be at least 225. So the sum of the squares cannot possibly be 135.

jan4dday · Answer

let the numbers be a, b, c, d and e.

SD^2 =   / 5 .. right?

this is = (a^2+ b^2+....+e^2) -30(a+b+c+d+e) + 225*5
 = 135 -30(75) + 1125
 = -990

when divided by 5 we get -198. the square root of which is abt 14

I am usually good at math but somewhere i have gone terribly wrong here. i cant seem to figure it out though

IanStewart · Answer

Your math is good - it's the data in the question which is impossible, as you've actually shown above; you cannot take the square root of a negative number (the root of -198 is undefined, not ~14), which demonstrates that no such set of numbers can exist.

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