Now, I can figure out question 1, but I cannot for the life of me figure out how you are supposed to get 2 and 3. Anyone have any ideas?
And don't worry, I'm not trying to cheat or anything. It's just a practice exame [smile]
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I had to do a pre-university practice exam today, and one of the questions was the following:
Now, I can figure out question 1, but I cannot for the life of me figure out how you are supposed to get 2 and 3. Anyone have any ideas?
And don't worry, I'm not trying to cheat or anything. It's just a practice exame [smile]
Now, I can figure out question 1, but I cannot for the life of me figure out how you are supposed to get 2 and 3. Anyone have any ideas?
And don't worry, I'm not trying to cheat or anything. It's just a practice exame [smile]
2. is almost a trick question, the 'x' column is actually the same as the bottom row, so x is 40.
3. is a little harder but the previous questions help. You already know K (7) and Q (9). From the bottom row you know that L+Z=24. Put this into the top row and you then know Z=13.
There's probably more than one way of doing 3), possibly simpler. If it helps, try and think of these questions as being analogous to simultaneous equations, it's not vital though. More importantly, remember that examiner's generally want to help you answer the question. Look for repeated letters, similar rows/columns etc.
Good luck with your exam =)
3. is a little harder but the previous questions help. You already know K (7) and Q (9). From the bottom row you know that L+Z=24. Put this into the top row and you then know Z=13.
There's probably more than one way of doing 3), possibly simpler. If it helps, try and think of these questions as being analogous to simultaneous equations, it's not vital though. More importantly, remember that examiner's generally want to help you answer the question. Look for repeated letters, similar rows/columns etc.
Good luck with your exam =)
4K = 28, so you know that K = 7
Then you used this to solve for Q, right?
Q + 3K = 30 (Or 2K + 2Q = 32)
Q + 21 = 30
Q = 9
So, filling in all the Qs and Ks in the chart, it simplifies into these equations:
Going down the rows:
L + 2Z = 37
Z + L = 24
Going across the columns:
L + Z = 14
Z + L + 16 = X
Z + 25 = Y
You can use the first two to solve for Z:
1)L = 37 - 2Z
2)L = 24 - Z
Combining: 37 - 2Z = 24 - Z
37 - 24 = 2Z - Z
13 = Z
and pluging that back into the first equation again you see that L = 1
So now you can easily solve for X and Y using the last two equations in the 'columns' list above.
[Edit - yeah, I can add. >.< Thanks Capn Midnight. I _think_ it's fixed now... o.O ]
[Edited by - sunandshadow on October 5, 2004 11:47:59 AM]
Then you used this to solve for Q, right?
Q + 3K = 30 (Or 2K + 2Q = 32)
Q + 21 = 30
Q = 9
So, filling in all the Qs and Ks in the chart, it simplifies into these equations:
Going down the rows:
L + 2Z = 37
Z + L = 24
Going across the columns:
L + Z = 14
Z + L + 16 = X
Z + 25 = Y
You can use the first two to solve for Z:
1)L = 37 - 2Z
2)L = 24 - Z
Combining: 37 - 2Z = 24 - Z
37 - 24 = 2Z - Z
13 = Z
and pluging that back into the first equation again you see that L = 1
So now you can easily solve for X and Y using the last two equations in the 'columns' list above.
[Edit - yeah, I can add. >.< Thanks Capn Midnight. I _think_ it's fixed now... o.O ]
[Edited by - sunandshadow on October 5, 2004 11:47:59 AM]
I got reallly lazy, so I just wrote a program to output two numbers that add up to a specific value that you enter, then I just substituted and came up with the right result (after solving normally for K and Q).
The sum of the rows must match the sum of the columns. So:
46 + 28 + 32 + 40 = 30 + 38 + x + y
Apparently there are many ways to solve this problem. If there were only one way, this information would be important.
46 + 28 + 32 + 40 = 30 + 38 + x + y
Apparently there are many ways to solve this problem. If there were only one way, this information would be important.
edit: rdfodra was first.
all is trivial and can be solved fast, without substitution.
1: you know that k*4=28, so K=7 Q=30-21=9
2: 40 because same as 4th row
3: is as dumb simple as all other. Summ of all cells in table. 30+38+40+y = 46+28+32+40
y = 46+28+32-30-38 = 38
all is trivial and can be solved fast, without substitution.
1: you know that k*4=28, so K=7 Q=30-21=9
2: 40 because same as 4th row
3: is as dumb simple as all other. Summ of all cells in table. 30+38+40+y = 46+28+32+40
y = 46+28+32-30-38 = 38
I've seen that type of question on the mensa test.
Basically, you can easily see that
k = 7 because 4(k) = 28;
then 3(k) + q = 30 is the same as 21 + q = 30 or q = 9;
then:
q + l + z + z == 46
l + 2z = 37;
and
l + z = 24;
Then do this:
| l + 2z = 37
| -1(l+z) = -1(24)
Now we can figure out the z by subtracting the two equations:
l - l cancels out
2z - z leaves us with z
37 - 24 gives us 13, so z = 13;
and since l + z = 24, l + 13 = 24, subtract z from 24 and l = 11.
So
Q = 9 (B)
X = 40 (A)
Y = 38 (B)
- heap
Basically, you can easily see that
k = 7 because 4(k) = 28;
then 3(k) + q = 30 is the same as 21 + q = 30 or q = 9;
then:
q + l + z + z == 46
l + 2z = 37;
and
l + z = 24;
Then do this:
| l + 2z = 37
| -1(l+z) = -1(24)
Now we can figure out the z by subtracting the two equations:
l - l cancels out
2z - z leaves us with z
37 - 24 gives us 13, so z = 13;
and since l + z = 24, l + 13 = 24, subtract z from 24 and l = 11.
So
Q = 9 (B)
X = 40 (A)
Y = 38 (B)
- heap
Solve[{Q + L + Z + Z == 46, K + K + K + K == 28, K + K + Q + Q == 32, K + Z + L + Q == 40, Q + K + K + K == 30, L + K + K + Z == 38, Z + K + Q + L == x, Z + K + Q + Q == y}, {Q, K, L, Z, x, y}]I pity people who use their brains.
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