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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 21:20
The units place in the expanded value of 97^275–32^44? 7 raise to any power has cyclicity of 7, 9 , 3, 1 as its unit digit 97^275 = 97^ (272+3) the unit digit for the result would be 3
Similarly, 2 raise to any power has cyclicity of 2, 4 , 8, 6 as its unit digit 32^44 the unit digit for the result would be 6
36 > 136> 7
Answer D



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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:01
We are only concerned about the digit in the units place. So, even in the above problem \(97^{275}– 32^{44}\) we can only be concerned about \(...7^{275} – ...2^{44}\)
The unit’s digit of powers of 7 are in order of 7, 9, 3, 1 Remainder of \(\frac{275}{4}\) = 3 The unit’s digit of the third power of 7 is 3. Thus, \(7^{275}\) will also have units digit of 3.
Similarly, The unit’s digit of powers of 2 are in order of 2, 4, 8, 6 Remainder \(\frac{44}{4}\) = 0 i.e 4 The unit’s digit of the fourth power of 2 is 6. Thus \(2^{44}\) will also have the unit’s digit of 6.
Hence, Unit’s digit of \(7^{275} – 2^{44}\) = Unit’s digit of \(97^{275} – 32^{44}\) = ….3  ….6 = …7
Answer: D



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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:03
Numbers ending with 7 will end with 7,9,3,1 based on the power. > Power cycle for 7 is 4. 97^275 will end with 3 since 275 when divided by 4 remainder is 3. Similarly, any number ending with 2 will have 2/4/8/6 in its unit;s digit based on the power. 32^44 will end with 6, as 44 when divided by 4 remainder is 0. Also, notice that 97^275 > 32^44. Hence, 97^275 32^44= .........3 ...........6=............7 OA is D
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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:03
A)1
I just tried to get the units digit of 7^5 2^4



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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:04
To solve this question we will use the pattern method.
We know that we can find the unit digit of any number from 0 to 9 by finding out if the power is of 4k+1, 4k+2, 4k+3 or 4k.
Using this we get that power 275 is of form 4k+3 and 44 is of form 4k.
Unit digit of 7 for power of form 4k+3 is 3 and unit of 2 for power of the form 4k is 6.
The difference between a number of X3 (where X any interger > 0) and 6 will be 7.
Hence, answer is 7.
Answer: D



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What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:16
Unit digit of 97^275 would be same as 7^275, which would be same as 7^3 (the unit digits of 7^x repeat after x = 4), which is 3. Similarly, unit digit of 32^44 would be same as 2^44, which would be same as 2^4 (the unit digits of 2^x repeat after x = 4), which is 6.
Now, ____3____6 will be same as 136 = 7 (where "____x" represents some number string ending with x) Hence, answer should be (D).



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What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:29
Quote: What is the digit on the units place in the expanded value of \(97^{275}–32^{44}\)?
A. 1 B. 3 C. 5 D. 7 E. 9 Unit digit of \(97^{275}–32^{44}\) = Unit digit of \(7^{275}–2^{44}\) CONCEPT: The unit digit of any number depends on the unit digit of the number so any digit other than unit digit is irrelevant such as \(97^{275}\) will have same unit digit as \(387^{275}\) or \(7^{275}\)Now, Unit digit of \(7^{275}–2^{44}\) = Unit digit of \(7^3–2^4\) CONCEPT: The cyclicity of unit digit of 7 and 2 is 4 i.e.e unit digits repeat after every 4th power. therefore Remainder (275/4) = 3 hence unit digit of \(7^275\) = unit digit of \(7^3\) Unit digit of \(7^3–2^4\) = 36 = 7 Answer: Option D
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What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:31
Unit digits for the powers of 97: 7, 9, 3, 1, 7, 9, 3........ and so on. Cyclicity = 4
Unit digits for the powers of 32: 2, 4, 8, 6, 2, 4, 8........ and so on. Cyclicity = 4
Now, for the 275th power of 97, unit digit will be "3". (275=68*4+3. So, 3rd term in the series [7,9,3,1])
For the 44th power of 32, unit digit will be "6". (44=11*4, 4th term in the series [2,4,8,6])
So, difference for any number with these unit digits will be "7". (X...X3  X..X6 = X..X7)
ANSWER : D



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What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 22:52
Last digit of the first no is 7 which a cyclicity of 4 . so last digit will be 3. Similarly last digit of second no is 4. So last digit will be 6. So effective last digit will be 36 =7



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Re: What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 23:16
Check for the cyclicity of 7 3M which means unit digit is going to be 3 and then cyclicity of 2 is 4M which means that the unit digit is going to be 6.
So 3  6 which means 13  6 = 7 Answer is D



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What is the digit on the units place in the expanded value of 97^275 –
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02 Jul 2019, 23:21
97^1, 97^5, 97^9, etc. have a units digit of 7 97^2, 97^6, 97^10, etc. have a units digit of 9 97^3, 97^7, 97^11, etc. have a units digit of 3 97^4, 97^8, 97^12, etc. have a units digit of 1
From the abovementioned pattern, one can deduce that 97^275 has a units digit of 3.
32^1, 32^5, 32^9, etc. have a units digit of 2 32^2, 32^6, 32^10,etc. have a units digit of 4 32^3, 32^7, 32^11,etc. have a units digit of 8 32^4, 32^8, 32^12,etc. have a units digit of 6
Similarly, one can deduce that 32^44 has a units digit of 6.
Therefore, the digit on the units place 97^275–32^44 is: ...3  ...6 = ...7
Answer is (D)
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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 00:52
7 follows a cycle of 4 and 2 follows a cycle of 4 The unit digit is of the two number is (32) =1



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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 01:23
97^275:Since the cyclicity is of 4 numbers(7,9,3,1), we can divide the power, 275, by 4 to get a remainder of 3. so the last digit will be 3 32^44:Since the cyclicity is of 4 numbers(2,4,8,6), we can divide the power, 44, by 4 to get a remainder of 0. so the last digit will be 6. so the answer should be 7



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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 01:25
What is the digit on the units place in the expanded value of 97275–3244 97 275 – 32 44 ?
A. 1 B. 3 C. 5 D. 7 E. 9
Since we are looking for the unit's place, let's figure out the unit's places of the numbers involved 97^275 will have 3 at the unit's place (formula: cyclicity of 4)
32^44 will have 6 at the unit's place (formula: cyclicity of 4)
Difference: _ _ _ 3  _ _ _ 6 = _ _ _ 7
IMO, answer is 7



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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 01:29
97275–3244
The last digit of the number 97^275 is defined by the the power of 7. The power of 7 has the cycle of 4 numbers (7, 9, 3, 1). => 275 = 4*68 + 3 => the last digit of the number 97^275 is 3. The last digit of the number 32^44 is defined by the the power of 2. The power of 2 has the cycle of 4 numbers (2, 4, 8, 6). => 44 = 4*11 => the last digit of the number 32^44 is 6.
XXX3  XXX6 = XXX7 = > Answer is D.



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What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 01:37
\(7^5\) = digit in the unit place would be 7(for square 9, for cube 3 and so on and so forth) \(2^4\) = digit in the unit place would be 6 (for square 4, for cube 8 and so on and so forth) therefore, 76(subtraction, since the last digit can be subtracted directly) would yield answer 1. Option A
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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 02:27
the first part is having units digit as 3, as 7 is having a cyclicity of 4,the power 275 when divided by 4, remainder is 3, so 7^3, last digit is 3;
similarly the second part is having units digit as 6, as cyclicity of 2 is 5, & 44 divided by 5 gives remainder as 4, 2^4, last digit will be 6;
subtraction of XXXX..X3YYY.YY6; last digit will be 7



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What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 02:51
Using the cyclical nature of unit digits raised to a power, we can easily calculate the answer. For units digit of 97^275, 7 is the units digit of 97. We know 7^1=7 7^2=9 (the units digit) 7^3=3 7^4=1 The units digits then repeat in 7,9,3,1 order. the power of 97, 275 is in the form of 4n+3. So 97^275 would have 3 as units digit.
For units digit of 32^44, 2 is the units digit of 32. We know 2^1=2 2^2=4 2^3=8 2^4=6(the units digit) The units digits then repeat in 2,4,8,6 order. the power of 32, 44 is in the form of 4n. So 32^44 would have 6 as units digit.
So the units digit of the substraction of these numbers would be = 36 Since 6 is bigger here than 3, 1 would carry over from the tens side to 3 making it 13. hence, 136=7 is the answer



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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 02:56
It's 7^2752^44
275/4 will.give a remainder of 3 , so units digit will 3
44/4 will.give a remainder of 0 , unit digit will be 2
32=1
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Re: What is the digit on the units place in the expanded value of 97^275 –
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03 Jul 2019, 03:25
imo 7,
question can be written as 7^3  2^4 so 36 gives ans 7




Re: What is the digit on the units place in the expanded value of 97^275 –
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