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What is the remainder, after division by 100, of 7^10 ? [#permalink]
 07 Oct 2011, 21:45
Question Stats:
77% (01:47) correct
22% (00:54) wrong based on 70 sessions
What is the remainder, after division by 100, of 7^10 ? (A) 1 (B) 7 (C) 43 (D) 49 (E) 70
Last edited by Bunuel on 14 Dec 2012, 02:13, edited 2 times in total.
Renamed the topic and edited the question.
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We have such a pattern
7
7*7=49
7*7*7=343
7*7*7*7=...1
7*7*7*7*7=7
So, the last number repeats every 5th time.
10/4 = 2, and remainder is 2.
we choose 7*7
it means that 7*7*7*7*7*7*7*7*7*7=.......49
We divide by 100, it means .....,49
where 49 is a remainder.
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kkalyan wrote: Previous Next
Help End Exam Review Section
What is the remainder, after division by 100, of 7^{10} ?
1
7
43
49
70
PLZ EXPLAIN THE TRICK IN SOLVING THIS TYPE REMAINDER PROBLEM Using Binomial theorem, last two digits of an exponent can be found as 7^(10)=7^(2*5)=49^5=(-1+50)^5=(-1)^5+5*(-1)^4*50=-1+50(Just considered last 2-digit of the product)=49 Look for Karishma's blogs. You may find more. Ans: "D"
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Re: PS: Remainder of 7^(10) divided by 100 [#permalink]
09 Oct 2011, 09:35
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kkalyan wrote: What is the remainder, after division by 100, of 7^{10} ?
(A) 1
(B) 7
(C) 43
(D) 49
(E) 70 7^4 is 2401 . So we can write 7^10 as ( 7^4 *7^4 * 7^2) divided by 100 .. This would give us (1*1*49)/ 100 which would give remainder as 49.
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Re: PS: Remainder of 7^(10) divided by 100 [#permalink]
14 Dec 2012, 01:48
if we do not hav formular, how do I do?
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Re: PS: Remainder of 7^(10) divided by 100 [#permalink]
14 Dec 2012, 02:21
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Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]
16 Dec 2012, 13:56
Hey Bunnel, this rule is general ? like if XXXXXX9^even the unit digit of the remainder is always 1 and XXXXX9^odd the unit digit of the remainder is always 9 ?? Thanks for your help
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Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]
16 Dec 2012, 23:39
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see wrote: Hey Bunnel,
this rule is general ? like if XXXXXX9^even the unit digit of the remainder is always 1 and XXXXX9^odd the unit digit of the remainder is always 9 ??
Thanks for your help The units digit of 9^even is 1 and the units digit of 9^odd is 9. If the units digit of a number is 1, then the remainder when this number will be divided by 100 will have the units digit of 1, for example 231 divided by 100 gives the reminder of 3 1. If the units digit of a number is 9, then the remainder when this number will be divided by 100 will have the units digit of 9, for example 239 divided by 100 gives the reminder of 3[b]9/b].
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Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]
18 Dec 2012, 00:14
what if the answer choise has another value with units digit 9? how do we need to proceed in that case?
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Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]
18 Dec 2012, 01:38
Ans: 7^10 can be written as 49^5 which can be written as (49^2)^2. 49 when divided by 100 it will give a remainder of (1)^2.49=49 answer (D).
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Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]
04 Feb 2013, 04:11
7 ^1 has last digit is 7
7^2 has last digit is 9
3
1
the last digit of 7^10 must be 9
the remainder must has the same last digit
only D fits
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Re: What is the remainder, after division by 100, of 7^10 ?
[#permalink]
04 Feb 2013, 04:11
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