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12 Feb 2018, 00:20
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (01:52) correct
13%
(02:18)
wrong
based on 42
sessions
History
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If Susan has $5 more than Tom, and if Tom has $2 more than Ed, which of the following exchanges will ensure that each of the three has an equal amount of money?
(A) Susan must give Ed $3 and Tom $1.
(B) Tom must give Susan $4 and Susan must give Ed $5.
(C) Ed must give Susan $1 and Susan must give Tom $1.
(D) Susan must give Ed $4 and Tom must give Ed $5.
(E) Either Susan or Ed must give Tom $7.
(A) Susan must give Ed $3 and Tom $1.
(B) Tom must give Susan $4 and Susan must give Ed $5.
(C) Ed must give Susan $1 and Susan must give Tom $1.
(D) Susan must give Ed $4 and Tom must give Ed $5.
(E) Either Susan or Ed must give Tom $7.
12 Feb 2018, 01:21
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S = T+5
T = E+2
Therefore, S = (E+2)+5 = E+7 and T = E+2
Now let us evaluate the answer options
(A) Susan must give Ed $3 and Tom $1.
S = E + 7-3-1= E+3 | T = E+2+1 = E+3 | Ed gets $3(E+3)
(B) Tom must give Susan $4 and Susan must give Ed $5.
T = E + 2 - 4 = E - 2 | S = E+7 - 5 = E+2 | Ed gets $5(E+5)
(C) Ed must give Susan $1 and Susan must give Tom $1.
Ed gives $1(E-1) | S = E+7-1 = E+6 | T = E+2+1 = E+3
(D) Susan must give Ed $4 and Tom must give Ed $5.
S = E+7-4 = E+3 | T = E+2 - 5 = E-3 | Ed gets $9(E+9)
(E) Either Susan or Ed must give Tom $7.
This in inconclusive as we will not get a correct answer!
Hence, Option A(Susan must give Ed $3 and Tom $1) will ensure the three of them have equal money.
T = E+2
Therefore, S = (E+2)+5 = E+7 and T = E+2
Now let us evaluate the answer options
(A) Susan must give Ed $3 and Tom $1.
S = E + 7-3-1= E+3 | T = E+2+1 = E+3 | Ed gets $3(E+3)
(B) Tom must give Susan $4 and Susan must give Ed $5.
T = E + 2 - 4 = E - 2 | S = E+7 - 5 = E+2 | Ed gets $5(E+5)
(C) Ed must give Susan $1 and Susan must give Tom $1.
Ed gives $1(E-1) | S = E+7-1 = E+6 | T = E+2+1 = E+3
(D) Susan must give Ed $4 and Tom must give Ed $5.
S = E+7-4 = E+3 | T = E+2 - 5 = E-3 | Ed gets $9(E+9)
(E) Either Susan or Ed must give Tom $7.
This in inconclusive as we will not get a correct answer!
Hence, Option A(Susan must give Ed $3 and Tom $1) will ensure the three of them have equal money.
13 Feb 2018, 18:08
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Bunuel
We can let S, T and E be the amount of money Susan, Tom and Ed have, respectively. We can create the equations:
S = T + 5
and
T = E + 2
Thus S = E + 2 + 5 = E + 7 and the sum of the three people, in terms of E, is E + 7 + E + 2 + E = 3E + 9. Thus if each have an equal amount of money, each will have E + 3. Now, let’s look at the options.
(A) Susan must give Ed $3 and Tom $1.
If Susan gives Ed $3 and Tom $1, she will have E + 7 - 3 - 1 = E + 3, Ed will have E + 3 and Tom will have E + 2 + 1 = E + 3. So each does have equal amount of money if Susan gives Ed $3 and Tom $1.
Alternate Solution:
Let’s assume that, at the start of the problem, Ed has $5, Tom has $7, and Susan has $12. The total amount of money is, therefore, 5 + 7 + 12 = 24. Each person needs to have the same amount of money, which is 24/3 = $8. Thus, Susan must give $3 to Ed and $1 to Tom.
Answer: A
