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26 Aug 2011, 02:29
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
71% (00:18) correct
29%
(00:35)
wrong
based on 23
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If 6 different numbers are to be selected from integers 0 to 6, how many 6-digit even integers greater than 300,000 can be composed?
OA:
OA:
1680
26 Aug 2011, 05:14
Kudos
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DeeptiM
Use the slot method:
(3)()()()()()
Let's fix 3 @ Hundred thousand place, which gives us just 1 option
Units place can be: 0,2,4,6(Total=4 options)=>(1)()()()()(4)
Now, 2-digits out of 7(0,1,2,3,4,5,6) are already taken; Thus, remaining can be 5;4;3;2
Tens=5: (1)()()()(5)(4)
Hundreds=4: (1)()()(4)(5)(4)
Thousands=3: (1)()(3)(4)(5)(4)
Ten Thousands=2: (1)(2)(3)(4)(5)(4)
Likewise for odd 5 @ Hundred thousand place.
Thus, for odds (3,5)@ Hundred thousand place: (2)(2)(3)(4)(5)(4)
However, for evens 4,6 @ Hundred thousand place, we will just have three options for units place(0,2,6) OR (0,2,4)
Options will look like: (1)(2)(3)(4)(5)(3)
Thus, for evens (4,6)@ Hundred thousand place: (2)(2)(3)(4)(5)(3)
Overall:
(2)(2)(3)(4)(5)(4)+(2)(2)(3)(4)(5)(3)=960+720=1680
Ans: "1680"
26 Aug 2011, 05:30
Kudos
Bookmarks
Hello ,
There are 1680 numbers possible
What is OA
My explanation is as follows,
Greater than 300,000: the possible numbers are 300,002 to 600,000+
The following cases need to be considered
Starting with number n >= 3and last number = {0,2,4,6}
case I :
Even number
4 or 6 in 100 thousands digit
the units digit can be any one of {0,2,4(if 6 is considered), 6 (if 4 is considered)}
so IF 4 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
So if 6 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
Hence in Case I we have 720
Case II
3 or 5 in 100 thousands digit
So if 3 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
So if 5 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
Hence For case II we have 480+480= 960
Total we have 960+720 = 1680 cases:
Consider Kudos if my explanation was helpful. Its a great option on GMATClub:
There are 1680 numbers possible
What is OA
My explanation is as follows,
Greater than 300,000: the possible numbers are 300,002 to 600,000+
The following cases need to be considered
Starting with number n >= 3and last number = {0,2,4,6}
case I :
Even number
4 or 6 in 100 thousands digit
the units digit can be any one of {0,2,4(if 6 is considered), 6 (if 4 is considered)}
so IF 4 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
So if 6 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
Hence in Case I we have 720
Case II
3 or 5 in 100 thousands digit
So if 3 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
So if 5 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
Hence For case II we have 480+480= 960
Total we have 960+720 = 1680 cases:
Consider Kudos if my explanation was helpful. Its a great option on GMATClub:
