SAT math Question[Numbers]

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1

<p>Grid in</p>

<p>x=the sum of all odd integers from 1 to 49, inclusive
y=the sum of all even integers from 2 to 50, inclusive
z=the sum of all integers from 1 to 48, inclusive</p>

<p>Based on the definitions of x, y, and z above, what is the value of
x+y-z?</p>

<p>This is taken from somebodys post on the xiggi thread. Xiggi states that 1 to 49 inclusive 2 to 50 inclusive is the same way as saying 1 to 50 inclusive. But how would you explain 1+2+3 and 2+3+4? things don't add up.</p>

<p>Does anyone have a method to solve these questions efficiently?</p>

2

<p>99?
z = sum of all odd and even numbers except 49 and 50 since it's only up to 48.</p>

<p>49+50 = 99</p>

3

<p>october 4th seems right. Basically imagine every single number being written out, and with the minus sign every number thats a double being crossed out. All that's left is 49+50.</p>

4

<p>right, but its asking for 1-49 + 2-50 inclusive. So dont we have to add from 1to 49 then add that sum to 2 to 50? That sum will be quite large! even if we subtract 1 +2+....48, shouldnt it be more than a mere 99?</p>

5

<p>But dont forget, its saying 1-49 ODD and 2-50 EVEN. Let me show you long way- the way I would do it. </p>

<p>1-50 all.
1+50=51
2+49=51
3+48=51</p>

<p>There are 25 pairs, so do 51x25 and you get 1275. </p>

<p>Subtact 1-48 all. </p>

<p>1+48=49
2+47=49
3+46= 49.
And there will be 24 pairs. 24x49=1176</p>

<p>1275-1176=99.</p>

6

<p>X+Y would equal all integers from 1-50 since x= all odds from 1-50( or 1-49) and y = all evens from 1-50.</p>

<p>so all integers from 1-48 (z) is subtracted from all intergers from 1-50. All integers from 1-48 cancel leaving 49 and 50.</p>

7

<p>Oh my effin god. I KEEP READING QUESTIONS WRONG! !!!<br>
:_(</p>

<p>Thanks alot guys!</p>

8

<p>here are some tricks you can use.</p>

<p>adding consecutive numbers ex. 1+2+3+4</p>

<p>(first term + last term) x 1/2 number of terms</p>

<p>(1+4) x (4/2) = 10</p>

<p>adding odd consecutive EX. 1+3+5+7</p>

<p>((first term+last term)/2)^2
((1+7)/2)^2
(8/2)^2
16</p>

<p>i forgot what it was for adding consecutive evens.</p>

9

<p>i think for consecutive evens its
(first term+last term)/2 x number of integers</p>

<p>not sure though</p>