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Questions from Veritas Prep Test

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Questions from Veritas Prep Test

by diegocuenca » Wed Jul 20, 2011 2:28 pm
I need some help with these

What is the value of x/y?
1. y = 4x + 3
2. 2x = 2y

Explanation
1 is NS because if x = -3/4 then y = 0 and x/y is undefined
2 is NS because if x = y = 0 then x/y is undefined
The statements together are S because together will allow us to solve for x = y = -1, therefore x/y = 1. C is correct.

Is the sum of a series of n consecutive integers even?
1. n = 6
2. The n digit number formed by the series is a mult. of nine

Explanation
1 is S because it gives enough information to solve since the sum can be express as: x + x+1 + x+2 + x+3 + x+4 + x+5 = 6x+15. 6x+15 must be odd since any even plus any odd number yields an odd #

What is the volume of rectangular box P in cubic centimeters?
1. The surface area of P is 54 sq. cm
2. P is a cube

Explanation
We need W, L, and H
1 tells us that 2WL + 2LH + 2HW = 54
2 tells us that W = L = H
Neither statement alone is S, combining them tells us that 6W^2 = 54 (where do they get the sq?)
W^2 = 9 => W = 3
Therefore the volume of the cube must be 3^3 = 27. C is correct.

If the prob. of rain on any given day in City x is 25%, what is the prob. that is rains on exactly 3 days in a 4 day period?

Explanation
p(rain any day) = 1/4
p(no rain any day) = 1 - (1/4) = 3/4
p(rain 3 out of 4 days) = (# of possible outcomes) x p(rain on 3 days) x p(no rain on 1 day), where did this equation come from? Seems like a very difficult ?

= C(4,3) x (1/4)^3 x (3/4) = 3/64. Choice C.

If x, y, and z are digits is (x + y + z) a mult. of 9?
1. The two digit number yz is a mult. of 9
2. If xyz is a three digit number, 3(xyz-1)+3 is a mult. of 9

Explanation
1 is NS for determining div. by 9
2 shows us that 3xyz is a mult. 9. Therefore, xyz must be a mult. of 3 but not necessarily a mult. of 9. None are S, E.
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by VivianKerr » Fri Jul 22, 2011 7:24 am
In the future, you'll probably get more help if you limit to 1-2 questions per post. :) Here's the first two:

Question 1

For the value of x/y, keep in mind that we don't know what x and y are. They could be integers, fractions, positives, negatives, or zero. If y is zero, then x/y is undefined since we can't have 0 in the denominator. Neither (1) nor (2) eliminates y = 0 as a possibility, so we can't know what the numerical value of x/y is with any certainty. If we COMBINE, however, we now have 2 equations with 2 variables. The "n equations with n variables" rule tells us we can solve for x and y and find actual values for each.

Question 2

Consecutive integers are like 1, 2, 3, 4, 15.... Notice how each term is +1 from the previous term. They are using "x" to stand for the first term, then "x + 1" to stand for the second term, etc. When they add them up, they get 6x + 15.

You also need to review properties of Odds/Evens. Let's say x is odd, such as 3. 3 x 6 = 18. 18 + 15 = 33, an odd number. Let's say x is even, such as 2. 2 x 6 = 12. 12 + 15 = 27, an odd number. So no matter what x is, the result will always be odd.
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by diegocuenca » Tue Jul 26, 2011 10:05 am
Thanks for the help, I really like the explanation for the first question. That is great. For the second question, why does the second premise not work? My guess is that it doesn't tell you anything about the sum.
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by Ashley@VeritasPrep » Tue Jul 26, 2011 8:42 pm
diegocuenca wrote:Thanks for the help, I really like the explanation for the first question. That is great. For the second question, why does the second premise not work? My guess is that it doesn't tell you anything about the sum.
The second statement does tell us *something* about the sum, because to say that a number is a multiple of 9 means that the sum of its digits will also be a multiple of 9 (divisibility rule for 9, I'm looking at you!). So we do know from (2) that the sum of the digits is a multiple of 9, but of course there are both even and odd multiples of 9. To further convince yourself, you can generate those series. If it's a one-digit number formed by the series, that number must just be 9 (odd sum). If, though, we want to generate an even sum (say 18), we can form a four-digit number that'll do so: 3456. And now we're at the point of having to say insufficient.
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by atuljadhav » Wed Jul 27, 2011 10:59 pm
For the second question, if the result is multiple of NINE that means it can be 9,18,27,36 which is either odd or even. Hence insufficient.
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by diegocuenca » Tue Aug 02, 2011 7:45 am
Thanks guys, I read the problem as saying that the UNITS digits is a multiple of nine, not the entire thing. Now that I see it means the entire number, it's clear to me. Silly mistake.
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by gmatboost » Tue Aug 02, 2011 6:13 pm
If the prob. of rain on any given day in City x is 25%, what is the prob. that is rains on exactly 3 days in a 4 day period?
While questions that sound similar to this do appear on the GMAT, questions exactly like this one do not. This is another example of an irresponsible practice question that is made difficult by using math that is not actually tested on the GMAT.

While it is true that
p(rain 3 out of 4 days) = (# of possible outcomes) x p(rain on 3 days) x p(no rain on 1 day)
...this formula is NOT in the OG math review and is NOT tested on the GMAT.

A question that might actually appear on the GMAT is:
If the prob. of rain on any given day in City x is 25%, what is the prob. that it rains on no more than 3 days in a 4 day period?

For this, you would need to find P(rain more than 3 days) = P(rain 4 days) = (1/4)^4 = 1/256 and then subtract from 1 to get P(rain 3 days or fewer). 1 - 1/256 = 255/256.
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by pinchharmonic » Wed Aug 03, 2011 11:52 pm
*im sorry, i think when it says the n digit number formed it means the numbers put next to one another, not the sum

Is the sum of a series of n consecutive integers even?
1. n = 6
2. The n digit number formed by the series is a mult. of nine

can someone explain what #2 is saying? does it mean that is n=1, then the sum of the series is a single digit number divisible by 9? Then if n=2, the sum of the series is a 2 digit number divisible by 9?

if that's the case then for n=1 the sum must be 9, i can think of 4,5 as the series. for n= 2 the two digit number could be 18, but what two consecutive integers add to 18?
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by pinchharmonic » Thu Aug 04, 2011 8:47 am
Ashley@VeritasPrep wrote:
diegocuenca wrote:Thanks for the help, I really like the explanation for the first question. That is great. For the second question, why does the second premise not work? My guess is that it doesn't tell you anything about the sum.
The second statement does tell us *something* about the sum, because to say that a number is a multiple of 9 means that the sum of its digits will also be a multiple of 9 (divisibility rule for 9, I'm looking at you!). So we do know from (2) that the sum of the digits is a multiple of 9, but of course there are both even and odd multiples of 9. To further convince yourself, you can generate those series. If it's a one-digit number formed by the series, that number must just be 9 (odd sum). If, though, we want to generate an even sum (say 18), we can form a four-digit number

that'll do so: 3456. And now we're at the point of having to say insufficient.
Ashley,

Does statement two require that the series be one digit? Because say the nth digit of the sum is 18, and n=1. That is divisible by 9 as a sum of its digits, as well as divisible by 9 taken as the number itself.

Also, you found a great example with he 3456 as that sums to 18, and itself is divisible by 9. Question is, a lot of other responders just mentioned that 18 is an even multiple of 9 without mentioning of finding an example. As a test taker, do we need to find a 4 digit series that sums to 18 or can we just assume one exists. This sorta ties with the first part of my problem because it lokos like the series has to be 1-digit.
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by gmatboost » Thu Aug 04, 2011 9:46 am
Is the sum of a series of n consecutive integers even?
1. n = 6
2. The n digit number formed by the series is a mult. of nine
Statement 2 is poorly phrased, because the series only forms an "n digit number" if each of the numbers is a single digit.

For example, if the sequence is 3, 4, 5, 6 then it has 4 terms and forms the 4-digit number 3456.
However, if the sequence is 13, 14, 15, 16 then it has 4 terms and forms the 8-digit number 13141516.
Or something like that... you wouldn't see phrasing like that on the test.

To answer your question about actually finding different examples, you definitely do need to do so. You can't assume there are sequences out there with even and odd sums that also "form" multiples of 9.
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by diegocuenca » Sat Aug 06, 2011 2:13 pm
As always, you guys are on your game.
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