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Here is this week’s problem:

A coin purse contains 13 coins, each worth 1, 5, 10, or 25 cents; the total value of the coins is 150 cents. How many 10-cent coins are in the purse?

(1) The 13 coins can be divided among five separate envelopes so that each envelope contains the same total monetary value.

(2) The 13 coins can be divided among six separate envelopes so that each envelope contains the same total monetary value.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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### One response to GMAT Challenge Problem Showdown: August 5, 2013

1. 25 cent – w
10 cent – x
5 cent – y
1 cent – z

so two equations will be

w + x + y + z = 13

25w + 10x + 5y + z = 150

but hit and trial you can come up with following possible combinations are -

A – w = 2, x = 9 , y = 2 and z = 0
or
B – w = 3, x = 5 , y = 5 and z = 0
or
C – w = 4, x = 1 , y = 8 and z = 0
or
D – w = 5, x = 1 , y = 2 and z = 5

now lets take the given statements,

Statement 1
all the money can be divided equally among 5 bag, i.e. each bag will contain 30 cent worth money.

so now let try to fix all the possible combinations

A is OK
B is OK
C is OK
D not OK
So can’t answer with surety so not SUFFICIENT.

Now statement 2.

all the money can be divided equally among 6 bag, i.e. each bag will contain 25 cent worth money.
so now let try to fix all the possible combinations
A not OK
B is OK
C is OK
D is OK
So can’t answer with surety so not SUFFICIENT.

Now combining two equation , we have B and C both combination satisfying the equation. Still not sure about the combination. Hence Can’t answer. Answer is E