The sum of n consecutive positive integers is 45

Two-digit numbers wx means positive integer, where w is the tens digit and x is the units digit: 10, 11, 12, ..., 99.

Two-digit numbers -wx means negative integer, where w is the tens digit and x is the units digit: -10, -11, -12, ..., -99.

Thank you I finally got what you are saying.

I think a variable representing an integer can be positive or negative ( or zero) , a variable without a minus sign does not mean that the variable is positive does it .

using the same logic
if a particular sum says

if a and b are integers what is b ?

1) a+b = 1
2) a= 2

From here can we say that a is positive ,because it is not -a ?
so a means = a is a positive integer
and -a means = a is a negative integer

In the same way when it says wx is a two digit integer , how can we say because it is not -wx hence wx is positive.

Thank you for your explanation ,

So the terms " Integer" and " Digit " makes all the difference ?They do not mean the same thing, right?

Integer =both negative , positive or zero
Digit = only 0 or positive.

I thought ( -2) was a digit too! a negative digit? Can we not have a negative digit?

Or is the Digit term in GMAT only used for non negative integers.

I think this is important info in terms of Gmat.

Really appreciate your help.Thank you so much .

Hi bunnel

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) x+3y=0 --> x and y have opposite signs --> either 4y=32 y=8 x=-3, xy=-24 OR -4y=32 y=-8 x=3 xy=24. The same answer. Sufficient..... how is x = -3, when y = 8?... isnt x=-3y??
(2) Multiple choices. Not sufficient.

There was a typo. Correct solution is below:

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.

Answer: A.

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.




////
Could you please explain for me what does unique non zero ?
>>> I feel that question is so silly but I had studied math in different language ( Arabic ) so I really have problem with many terms

second question is WHY you said aaa=37 k I could not undersand from where it comes
Thank you a lot I learn from here a lot of useful things .

Digits are ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Non-zero digits are all of them except 0: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Unique means that w,x and c are are all different from one another. Thus w, x and c are unique non-zero digits of the two digit numbers wx and cx means that w, x, and c are 1, 2, 3, 4, 5, 6, 7, 8, or 9.

As for 37k, each of the numbers 111, 222, ..., 999 are multiples of 37.

Hope it's clear.

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-n ... 26861.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-a-product ... 63139.html


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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-multiplic ... 63142.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-y-x-posit ... 03882.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-a-and-b-a ... 40295.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-m-and-n-a ... 05308.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-b-c-and-d ... 05823.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-and-y-a ... 82076.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-the-integ ... 91399.html


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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-n ... 63143.html