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# If a, b, c, and d are positive integers, what is the value..

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If a, b, c, and d are positive integers, what is the value..  [#permalink]

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Updated on: 22 Dec 2012, 08:31
1
9
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Difficulty:

35% (medium)

Question Stats:

66% (01:21) correct 34% (01:26) wrong based on 324 sessions

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If a, b, c, and d are positive integers, what is the value of (a + b)(c + d)?

(1) 4a! = b!
(2) 5c! = d!

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Originally posted by daviesj on 22 Dec 2012, 07:46.
Last edited by daviesj on 22 Dec 2012, 08:31, edited 1 time in total.
Manager
Status: Never ever give up on yourself.Period.
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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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22 Dec 2012, 08:25
4
1
700+ questions are never much difficult,they are just tricky...

In this problem if you can see carefully, only one combination of a and b satisfies 4a! = b!...well, how's that?
simple for a=3... a! will be 3*2*1 and 4*a! will be 4*3*2*1 i.e. 4! so b=4...no other value of a would satisfy this..
Same is the case with 5c! = d! .i.e c=4 and d=5.

Sentence 1: not sufficient as it gives only the values of a & b
Sentence 2: not sufficient as it gives only the values of c & d

both sentences together: can solve the problem as we get all the values

Hope the point is clear..:)
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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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22 Dec 2012, 08:06
I just stumbled onto the "!" symbol in math, so I cannot solve this problem. However I've got a question!

(Let's say a = 2)
When it was 4a!, does that equal 4*1*2, or does it equal 1*2*1*2*1*2*1*2?

I'm a bit confused as of which order to do things.
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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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22 Dec 2012, 08:22
1
If a, b, c, and d are positive integers, what is the value of (a + b)(c + d)?
(1) 4a! = b!
(2) 5c! = d!

Hi,

Statement 1: 4a! = b! so (a,b) have only one valid case (3,4) so values are a=3 and b=4
Statement 1: 5c! = d! so (c,d) have only one valid case (4,5) so values are c=4 and b=5

Ans: (3+4)(4+5) => 7*9

C
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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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23 Dec 2012, 04:28
If a, b, c, and d are positive integers, what is the value of (a + b)(c + d)?
(1) 4a! = b!
(2) 5c! = d!
all u need to know are values of positive integers a,b,c &d.
statement1:talks about only a and b .no info reg c&d .insuff
statement2:talks about only c&d.no info reg a&b.insuffi.
combining 1 &2
only values which will work for a&b are a=3,b=4,c&d are c=4,d=5.sufficient.
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Re: If a,b,c,and d are positive integers,what is the value of  [#permalink]

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02 Mar 2013, 19:27
We are given that a,b,c, and d are positive integers and need to find the value of (a+b) (c+d)

Consider statement (1) first
4a! = b!
This can only be true if a=3 and b=4. However this does not give us the value of c and d and is insufficient.

Consider statement (2) next
5c! = d!
This can only be true if d=5 and c=4. However this does not give us the value and a and b and is insufficient.

Combining both, we have the values of a,b,c, and d. Sufficient.

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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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29 Nov 2016, 05:22
4a!=b! means (b!/a!)=4, the only possibility is 4!/3!

5c!=d! means (d!/c!)=5, the only possibility is 5!/4!

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Re: If a, b, c, and d are positive integers, what is the value..  [#permalink]

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17 Jan 2018, 05:29
Hello from the GMAT Club BumpBot!

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Re: If a, b, c, and d are positive integers, what is the value..   [#permalink] 17 Jan 2018, 05:29
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