Verbal Reasoning - Arithmetic Reasoning - Discussion

Let's denote the number of cards each player has as follows:

- ( A ) has ( a ) cards
- ( B ) has ( b ) cards
- ( C ) has ( c ) cards
- ( D ) has ( d ) cards
- ( E ) has ( e ) cards

From the problem, we can derive the following equations based on the statements made:

1. From A's statement to B:
If B gives A 3 cards, then B will have ( b - 3 ) cards and A will have ( a + 3 ) cards. The equation becomes:
b - 3 = a + 3
and b = a + 6 =>Equation 1.

2. From A's statement about D:
- If D takes 5 cards from B, then D will have ( d + 5 ) cards and B will have ( b - 5 ) cards.
The equation becomes:
d + 5 = e
And d = e - 5 =>Equation 2.

3. From A and C together have twice as many cards as E:
a + c = 2e => Equation 3.

4. From B and D together have the same number of cards as A and C:
b + d = a + c => Equation 4.

5. Total number of cards:
a + b + c + d + e = 150 => Equation 5.

Step 1: Substitute Equations
Now, we will substitute Equations 1 and 2 into the other equations.

From Equation 1:
b = a + 6

And From Equation 2:
d = e - 5

Step 2: Substitute into Equation 4:
Substituting ( b ) and ( d ) into Equation 4:
(a + 6) + (e - 5) = a + c.

This simplifies to:
a + 6 + e - 5 = a + c
=> e + 1 = c
And c = e + 1 => Equation 6.

Step 3: Substitute into Equation 3
Now substitute ( c ) from Equation 6 into Equation 3:
a + (e + 1) = 2e

This simplifies to:
a + e + 1 = 2e
a + 1 = e
And e = a + 1 => Equation 7


Step 4: Substitute into Equation 5

Now substitute ( b ), ( d ), and ( e ) into Equation 5:
a + (a + 6) + (e + 1) + (e - 5) + e = 150

Substituting ( e = a + 1 ) into the equation:
a + (a + 6) + ((a + 1) + 1) + ((a + 1) - 5) + (a + 1) = 150

This simplifies to:
a + (a + 6) + (a + 2) + (a - 4) + (a + 1) = 150.

Combining like terms:
5a + 6 + 2 - 4 + 1 = 150,
=> 5a + 5 = 150.

Thus:
5a = 145
=> a = 29.


Step 5: Find ( e ) and ( c )
Now, using Equation 7 to find ( e ):
e = a + 1 = 29 + 1 = 30

Using Equation 6 to find (c ):
c = e + 1 = 30 + 1 = 31

Conclusion:
Thus, the number of cards that C has is 31.

A + 3 = B - 3 is the first condition; since A asks B to give 3 cards so that they have equal number of cards.

Therefore, the answer is C has 31 cards.

A ask the B to give 3 card. So, that B will have as much as A in this moment. That means A is not received 3 card in this moment.

That is, answer is 28.

I think the answer is incorrect.

In the first, it should be A + 3 = B - 3 but not A = B - 3 then answer becomes C = 31 NOT 28 because he asked at this momment when B is giving three cards to A then B have B - 3 and A have A + 3 and said it is equal.

Putting E = 30 and D = 25 in (iv), we get:B = 35. How 35 comes?

How this D+5 = E came?

What I think is - B gave his five cards to D therefore D = B+5;