Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Aug 2015, 07:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sum of n consecutive positive integers is 45

Author Message
TAGS:
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [17] , given: 7400

The sum of n consecutive positive integers is 45 [#permalink]  16 Oct 2009, 18:59
17
KUDOS
Expert's post
26
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

39% (01:51) correct 61% (01:17) wrong based on 124 sessions
Please find below new set of DS problems:

TIP: many of these problems act in GMAT zone, so beware of ZIP trap.

1. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

2. Is a product of three integers XYZ a prime?
(1) X=-Y
(2) Z=1

3. Multiplication of the two digit numbers wx and cx, where w,x and c are unique non-zero digits, the product is a three digit number. What is w+c-x?
(1) The three digits of the product are all the same and different from w c and x.
(2) x and w+c are odd numbers.

4. Is y – x positive?
(1) y > 0
(2) x = 1 – y

5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

6. If M and N are integers, is (10^M + N)/3 an integer?
1. N = 5
2. MN is even

7. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

8. If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16

9. Is the integer n odd
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n

10. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is odd
(2) n >= 9

OA and explanations to follow.

Also you can check new set of PS problems: good-set-of-ps-85414.html
_________________

Last edited by Bunuel on 16 Oct 2009, 21:33, edited 1 time in total.
 Kaplan Promo Code Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 61

Kudos [?]: 593 [1] , given: 19

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 21:14
1
KUDOS
Bunuel wrote:
1. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

1. n could be 2 or 6 or 10
a + a+1 = 45
a = 22
n = 2

a + a+1 + a+2 + a+3 + a+4 + a+5 = 45
a = 5
n = 6

2. n could be 2, 3, 5 or 6

1&2: n could be 2 or 6. E.

Bunuel wrote:
10. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n >= 9

1. n could be 2 or 6 or 10

n = 2:
a + a+1 = 45
a = 22

n = 6:
a + a+1 + a+2 + a+3 + a+4 + a+5 = 45
a = 5

2. n could be 9 or 10 or 14 or 15 or 18 & so on...

1&2: n could be 10 or 14 or 18. E.
_________________
Senior Manager
Joined: 31 Aug 2009
Posts: 420
Location: Sydney, Australia
Followers: 6

Kudos [?]: 165 [1] , given: 20

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 21:55
1
KUDOS
Bunuel wrote:
TIP: many of these problems act in GMAT zone, so beware of ZIP trap.

1. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

2. Is a product of three integers XYZ a prime?
(1) X=-Y
(2) Z=1

What is the ZIP trap?

Q1)
Statement 1) n = 2,4,6 etc
n = 2 => x+(x+1)=45 => x=22 (works)
n = 4 => x+(x+1)+(x+2)+(x+3)=45 => 4x+6=45 => x=39/4 (doesn't work)
n = 6 => Take above equation+(x+4)+(x+5) => 6x+15=45 => x=5 (works)
Not suff.
Statement 2) n < 9. This is proven insufficient from the working above since both n=2 and n=6 n<9.
1 and 2 together still prove insufficient due to above working.

ANS = E.

Q2)
Statement 1) X=-Y
This means Z needs to be negative and for XYZ to have a chance of being prime. Z can be anything.
Insufficient.
Statement 2) Z=1
X and Y could be anything such as 2 and 3 (non prime multiple) or 1 and 2 (prime).
Insufficient.
1 and 2 Together) Z = 1. X=-Y
1*Y*(-Y) = -Y^2 which cannot be prime as it is negative.

ANS = C

Edited: Got the right working but wrote E instead of C. I gotta stop doing that

Last edited by yangsta8 on 16 Oct 2009, 22:03, edited 1 time in total.
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 61

Kudos [?]: 593 [0], given: 19

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 22:01
Bunuel wrote:
2. Is a product of three integers XYZ a prime?

(1) X=-Y
(2) Z=1

(1) If x=-y = 2 and z = -1, yes. Otherwise, no..
(2) If z = 1, x could be 2 and y = 1. xyz is a price. If something else, no.

From 1 and 2: x = -y and z = 1, xyz is always a -ve integer, which cannot be a prime....C.
_________________
Senior Manager
Joined: 31 Aug 2009
Posts: 420
Location: Sydney, Australia
Followers: 6

Kudos [?]: 165 [0], given: 20

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 22:03
Bunuel wrote:
4. Is y – x positive?
(1) y > 0
(2) x = 1 – y

Statement 1) y>0 Not suff, X could be anything larger or smaller than X.
Statement 2) x=1-y
x+y=1
Let x=3 and y=-2 then y-x < 0.
But if x=1/4 and y=3/4 then y-x >0
Not suff.

1 and 2 together)
From the example above we have:
if x=1/4 and y=3/4 then y-x >0
but if we flip it around:
if x=3/4 and y=1/4 then y-x <0
not suff.

ANS = E
Senior Manager
Joined: 31 Aug 2009
Posts: 420
Location: Sydney, Australia
Followers: 6

Kudos [?]: 165 [1] , given: 20

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 22:13
1
KUDOS
Bunuel wrote:
6. If M and N are integers, is (10^M + N)/3 an integer?
1. N = 5
2. MN is even

Statement 1) N=5
If M>=0 then it is always divisible by 3. Since the number will always consist of 1, trailing 0's and a 5. Of which the sum of digits =6 which is the rule for divisibility by 3.
If M<0 then the equation is not divisble by 3. For example if M=-1.
Insufficient

Statement 2) MN is even. Again this means M could still be negative so insufficient. For example M could be -1 and N could be 2 which is not divisible by 3. Or n=5 but m=-2 which is not.

Statements together) Still insuff. m=2 n=5 works. But m=-2 n=5 doesn't work.

ANS = E
Senior Manager
Joined: 31 Aug 2009
Posts: 420
Location: Sydney, Australia
Followers: 6

Kudos [?]: 165 [0], given: 20

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 22:17
Bunuel wrote:
7. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

Expanding it out we get :
x^2 + bx + c = x^2 + 2dx + d^2

Statement 1) d = 3
d^2 = c = 9
Suff.
Statement 2) b=6
b=6=2d
d=3
d^2=c=9
Suff

ANS = D
Senior Manager
Joined: 31 Aug 2009
Posts: 420
Location: Sydney, Australia
Followers: 6

Kudos [?]: 165 [0], given: 20

Re: Good set of DS 3 [#permalink]  16 Oct 2009, 22:41
Bunuel wrote:
9. Is the integer n odd
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n

10. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is odd
(2) n >= 9

Q9)
Statement 1)
N is a multiple of 3. N could be 3 or 6.
Insufficient.
Statement 2)
I am not sure how to prove this except by examples:
Example 1:n=9 factors={1,3,9}, 2n=18 factors={1,2,3,6,9,18}
N is odd is true.
Example 2:n=6 factors={1,2,3,6} 2n=12 factors={1,2,3,4,6,12} Does not have twice as many factors.
Example 3: n=3 factors={1,3} 2n=6 factors={1,2,3,6}
N is odd is true.

ANS = B

Q10)
Statement 1) N is odd.
N could be 1. 45
N could also be 3. x+(x+1)+(x+2)=45 => 3x=42 x=14
Insufficient.
Statement 2) N>=9
Let n=9.
9x+8+7+6+5+4+3+2+1=45 => 9x+36=45 => 9x=9 x=1
we cannot use n>10 because adding anymore positive integers means sum > 45.
Sufficient.

ANS = B
Director
Joined: 01 Apr 2008
Posts: 903
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 18

Kudos [?]: 360 [0], given: 18

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 00:09
Hi Bunuel, Awesome questions...keep them coming esp DS
+1 to you.
Manager
Joined: 01 Jan 2009
Posts: 96
Location: India
Schools: LBS
Followers: 2

Kudos [?]: 63 [2] , given: 6

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 01:50
2
KUDOS
Bunuel wrote:
3. Multiplication of the two digit numbers wx and cx, where w,x and c are unique non-zero digits, the product is a three digit number. What is w+c-x?
(1) The three digits of the product are all the same and different from w c and x.
(2) x and w+c are odd numbers.

WX x CX = IJK

1.) I,J,K are the same and not equal to W,C or X.

so 3 digit numbers with all digit same are 111,222,...., 999.

basically multiples of 111 (37x3).

so we get 1 number = 37

conditions the second number has to meet = last digit = 7, multiple of 3, double digit.

so we get 27.

27 x 37 = 999

So suff.

2.) x and w+c are odd.

this gives multiple values.

So A.
_________________

The Legion dies, it does not surrender.

Manager
Joined: 01 Jan 2009
Posts: 96
Location: India
Schools: LBS
Followers: 2

Kudos [?]: 63 [1] , given: 6

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 01:57
1
KUDOS
Bunuel wrote:
5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

|a|b > 0?

|a| is always +ve. So we need to know if b is +ve or -ve.

1.) mod of any number is +ve. Insuff.

2.) |a|^b is an integer.

we know a and b are integers.

so |a| is a +ve integer.

any +ve integer raised to a -ve integer will give us a fraction.

e.g. 4 ^ -3 = 1/ (4^3)

which will never be an integer.

so for |a|^b to be an integer b has to be +ve.

So its suff.

So B.
_________________

The Legion dies, it does not surrender.

Manager
Joined: 01 Jan 2009
Posts: 96
Location: India
Schools: LBS
Followers: 2

Kudos [?]: 63 [0], given: 6

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 02:06
Bunuel wrote:
8. If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16

1.) -4x = 12y
or -x = 3y

so we get x and y to be = 24,-8 or -24,8

xy = -192 in both cases

so suff.

2.) |x| - |y| = 16

we can get |x| and |y|.

but the signs of x and y cannot be determined. So insuff.

IMO A.
_________________

The Legion dies, it does not surrender.

Manager
Joined: 08 Oct 2009
Posts: 66
Followers: 1

Kudos [?]: 21 [0], given: 5

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 04:38
Great questions, keep em coming ..
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [2] , given: 7400

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 09:24
2
KUDOS
Expert's post
jax91 wrote:
Bunuel wrote:
5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

|a|b > 0?

|a| is always +ve. So we need to know if b is +ve or -ve.

1.) mod of any number is +ve. Insuff.

2.) |a|^b is an integer.

we know a and b are integers.

so |a| is a +ve integer.

any +ve integer raised to a -ve integer will give us a fraction.

e.g. 4 ^ -3 = 1/ (4^3)

which will never be an integer.

so for |a|^b to be an integer b has to be +ve.

So its suff.

So B.

This is not correct.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [0], given: 7400

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 09:29
Expert's post
jax91 wrote:
Bunuel wrote:
3. Multiplication of the two digit numbers wx and cx, where w,x and c are unique non-zero digits, the product is a three digit number. What is w+c-x?
(1) The three digits of the product are all the same and different from w c and x.
(2) x and w+c are odd numbers.

WX x CX = IJK

1.) I,J,K are the same and not equal to W,C or X.

so 3 digit numbers with all digit same are 111,222,...., 999.

basically multiples of 111 (37x3).

so we get 1 number = 37

conditions the second number has to meet = last digit = 7, multiple of 3, double digit.

so we get 27.

27 x 37 = 999

So suff.

2.) x and w+c are odd.

this gives multiple values.

So A.

Though answer is right and one number indeed is 37, but it was not the only possibility for it. So you got the right answer with right numbers, but missed one case to consider.
_________________
Director
Joined: 01 Apr 2008
Posts: 903
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 18

Kudos [?]: 360 [0], given: 18

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 09:33
5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

Basically the question asks, is b>0?

stmt1: b can be -ve or +ve or 0. Insuff.
stmt2: b can be +ve or 0. Insuff.
Combining, b can be +ve or 0. Insuff.

E.
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [8] , given: 7400

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 16:29
8
KUDOS
Expert's post
2
This post was
BOOKMARKED

1. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

(1) n=2 --> 22+23=45, n=4 --> n=6 x1+(x1+1)+(x1+2)+(x1+3)+(x1+4)+(x1+5)=45 x1=5. At least two options for n. Not sufficient.
(2) n<9 same thing not sufficient.
(1)+(2) No new info. Not sufficient.

2. Is a product of three integers XYZ a prime?
(1) X=-Y
(2) Z=1

(1) x=-y --> for xyz to be a prime z must be -p AND x=-y shouldn't be zero. Not sufficient.
(2) z=1 --> Not sufficient.
(1)+(2) x=-y and z=1 --> x and y can be zero, xyz=0 not prime OR xyz is negative, so not prime. In either case we know xyz not prime.

3. Multiplication of the two digit numbers wx and cx, where w,x and c are unique non-zero digits, the product is a three digit number. What is w+c-x?
(1) The three digits of the product are all the same and different from w c and x.
(2) x and w+c are odd numbers.

(1) wx+cx=aaa (111, 222, ... 999=37*k) --> As x is the units digit in both numbers, a can be 1,4,6 or 9 (2,3,7 out because x^2 can not end with 2,3, or 7. 5 is out because in that case x also should be 5 and we know that x and a are distinct numbers).
1 is also out because 111=37*3 and we need 2 two digit numbers.
444=37*12 no good we need units digit to be the same.
666=37*18 no good we need units digit to be the same.
999=37*27 is the only possibility all digits are distinct except the unit digits of multiples.
Sufficient
(2) x and w+c are odd numbers.
Number of choices: 13 and 23 or 19 and 29 and w+c-x is the different even number.

4. Is y – x positive?
(1) y > 0
(2) x = 1 – y

Easy one even if y>0 and x+y=1, we can find the x,y when y-x>0 and y-x<0

5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

This is tricky |a|b > 0 to hold true: a#0 and b>0.

(1) |a^b|>0 only says that a#0, because only way |a^b| not to be positive is when a=0. Not sufficient. NOTE having absolute value of variable |a|, doesn't mean it's positive. It's not negative --> |a|>=0

(2) |a|^b is a non-zero integer. What is the difference between (1) and (2)? Well this is the tricky part: (2) says that a#0 and plus to this gives us two possibilities as it states that it's integer:
A. -1>a>1 (|a|>1), on this case b can be any positive integer: because if b is negative |a|^b can not be integer.
OR
B. |a|=1 (a=-1 or 1) and b can be any integer, positive or negative.
So (2) also gives us two options for b. Not sufficient.

(1)+(2) nothing new: a#0 and two options for b depending on a. Not sufficient.

6. If M and N are integers, is (10^M + N)/3 an integer?
(1) N = 5
(2) MN is even

Note: it's not given that M and N are positive.
(1) N=5 --> if M>0 (10^M + N)/3 is an integer ((1+5)/3), if M<0 (10^M + N)/3 is a fraction ((1/10^|M|+5)/3). Not sufficient.
(2) MN is even --> one of them or both positive/negative AND one of them or both even. Not sufficient
(1)+(2) N=5 MN even --> still M can be negative or positive. Not sufficient.

7. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

Note this part: "for all values of x"
So, it must be true for x=0 --> c=d^2 --> b=2d
(1) d = 3 --> c=9 Sufficient
(2) b = 6 --> b=2d, d=3 --> c=9 Sufficient

8. If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x-12y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs.

So either: $$|x|=x$$ and $$|y|=-y$$ --> in this case $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$;

OR: $$|x|=-x$$ and $$|y|=y$$ --> $$|x|+|y|=-x+y=3y+y=4y=32$$ --> $$y=8$$ and $$x=-24$$ --> $$xy=-24*8$$, the same answer.

Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

9. Is the integer n odd
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n

(1) 3 or 6. Clearly not sufficient.
(2) TIP:
When odd number n is doubled, 2n has twice as many factors as n.
Thats because odd number has only odd factors and when we multiply n by two we remain all these odd factors as divisors and adding exactly the same number of even divisors, which are odd*2.

Sufficient.

10. The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is odd
(2) n >= 9

Look at the Q 1 we changed even to odd and n<9 to n>=9

(1) not sufficient see Q1.
(2) As we have consecutive positive integers max for n is 9: 1+2+3+...+9=45. (If n>9=10 first term must be zero. and we are given that all terms are positive) So only case n=9. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [13] , given: 7400

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 16:44
13
KUDOS
Expert's post
Yes and about the ZIP trap:

GMAT likes to act in the zone -1<=x<=1. So I always ask myself:

Did I assumed, with no ground for it, that variable can not be Zero? Check 0!
Did I assumed, with no ground for it, that variable is an Integer? Check fractions!
Did I assumed, with no ground for it, that variable is Positive? Check negative values!

I called it ZIP trap. Helps me a lot especially with number property problems.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49628 [0], given: 7400

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 17:48
Expert's post
You can check new set of:
DS problems: new-set-of-good-ds-85441.html#p640158
PS problems: new-set-of-good-ps-85440.html#p640145
_________________

Last edited by Bunuel on 17 Oct 2009, 19:40, edited 1 time in total.
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 61

Kudos [?]: 593 [0], given: 19

Re: Good set of DS 3 [#permalink]  17 Oct 2009, 18:14
Bunuel wrote:
Yes and about the ZIP trap:

GMAT likes to act in the zone -1<=x<=1. So I always ask myself:

Did I assumed, with no ground for it, that variable can not be Zero? Check 0!
Did I assumed, with no ground for it, that variable is an Integer? Check fractions!
Did I assumed, with no ground for it, that variable is Positive? Check negative values!

I called it ZIP trap. Helps me a lot especially with number property problems.

Thats cool.

You can say PINZF (or better) trap as well:

P = positive
I = integer
N = negative
Z = zero
F = fraction
_________________
Re: Good set of DS 3   [#permalink] 17 Oct 2009, 18:14

Go to page    1   2   3   4   5   6    Next  [ 103 posts ]

Similar topics Replies Last post
Similar
Topics:
12 If m and n are consecutive positive integers, is m greater t 11 12 Feb 2014, 01:04
4 If the sum of n consecutive integers is 1, where n > 1 3 24 Oct 2012, 13:18
9 The sum of n consecutive positive integers is 45. What is 12 31 Jan 2012, 16:42
4 If m and n are consecutive positive integers, is m greater 4 19 Jan 2012, 10:09
9 The sum of n consecutive positive integers is 45. What is 37 04 Apr 2008, 19:08
Display posts from previous: Sort by