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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (02:18) correct
40%
(02:19)
wrong
based on 144
sessions
History
Date
Time
Result
Not Attempted Yet
If n is positive integer, what is the units digit of n?
(1) n^2 - 25n + 150 < 0
(2) n^2 and n^5 have the same units digit
(1) n^2 - 25n + 150 < 0
(2) n^2 and n^5 have the same units digit
08 Feb 2022, 09:07
Kudos
Bookmarks
Here is the OE
Solution:
Step 1: Analyse Question Stem
• We know n is a positive integer.
• We need to find the units digit of n.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: \(n^2\) -25n + 150 < 0
\(n^2\) -25n + 150 < 0
⟹ \(n^2\) -10n – 15n + 150 < 0
⟹ (n – 10) (n – 15) < 0
⟹ 10 < n < 15
Thus, n can be 11, 12, 13, or 14.
Since we are not getting a unique value of n, statement 1 is not sufficient to answer the question. We can eliminate answer options A and D.
Statement 2: n2 and n5 have the same units digit
If \(n^2\) and \(n^5\) have the same units digit, then the units digit of n can be
• Units digit of n = 0
• Units digit of n = 1
• Units digit of n = 5
• Units digit of n = 6
Since, we are not getting a unique units digit, statement 2 is also not sufficient to answer the question. And we can eliminate answer option B.
Step 3: Analyse Statements by Combining
From statement 1: n can be 11, 12, 13, or 14
From statement 2: the units digit of n can be 0, 1, 5, or 6
Combining, we can say that n has to be 11.
Thus, the correct answer is Option C.
Solution:
Step 1: Analyse Question Stem
• We know n is a positive integer.
• We need to find the units digit of n.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: \(n^2\) -25n + 150 < 0
\(n^2\) -25n + 150 < 0
⟹ \(n^2\) -10n – 15n + 150 < 0
⟹ (n – 10) (n – 15) < 0
⟹ 10 < n < 15
Thus, n can be 11, 12, 13, or 14.
Since we are not getting a unique value of n, statement 1 is not sufficient to answer the question. We can eliminate answer options A and D.
Statement 2: n2 and n5 have the same units digit
If \(n^2\) and \(n^5\) have the same units digit, then the units digit of n can be
• Units digit of n = 0
• Units digit of n = 1
• Units digit of n = 5
• Units digit of n = 6
Since, we are not getting a unique units digit, statement 2 is also not sufficient to answer the question. And we can eliminate answer option B.
Step 3: Analyse Statements by Combining
From statement 1: n can be 11, 12, 13, or 14
From statement 2: the units digit of n can be 0, 1, 5, or 6
Combining, we can say that n has to be 11.
Thus, the correct answer is Option C.
06 Aug 2022, 22:03
Kudos
Bookmarks
If n is a positive integer, what is the units digit of n?
(1) \(n^2\) - 25n + 150 < 0
\((n-10)(n-15)<0\)
Here, n between 10 and 15 will give n-10 as positive and n-15 as negative. Thus their product will be negative.
Hence, n can be 11, 12, 13 or 14.
Different answers - 1, 2, 3 or 4.
Insufficient
(2) \(n^2 \) and \(n^5\) have the same units digit.
We know that units digit repeat after every 4 consecutive powers.
Thus, \(n^1\) and \(n^5\) will have same unit’s digit.
So, the statement becomes ‘ \(n^2 \) and \(n^1\) have the same units digit.’
This means consecutive powers have same digits.
Now, the units digit of 0 are always same. \(0^1=0…0^2=0\)
Similarly units digit of integer ending with 1 \(1^1=1…1^2=1\)
Others are \(5^1=5….5^2=25\) and \(6^1=6……6^2=36\)
Hence, possible answers - 0, 1, 5 and 6.
Insufficient
Combined
Answer is 1.
Sufficient
C
(1) \(n^2\) - 25n + 150 < 0
\((n-10)(n-15)<0\)
Here, n between 10 and 15 will give n-10 as positive and n-15 as negative. Thus their product will be negative.
Hence, n can be 11, 12, 13 or 14.
Different answers - 1, 2, 3 or 4.
Insufficient
(2) \(n^2 \) and \(n^5\) have the same units digit.
We know that units digit repeat after every 4 consecutive powers.
Thus, \(n^1\) and \(n^5\) will have same unit’s digit.
So, the statement becomes ‘ \(n^2 \) and \(n^1\) have the same units digit.’
This means consecutive powers have same digits.
Now, the units digit of 0 are always same. \(0^1=0…0^2=0\)
Similarly units digit of integer ending with 1 \(1^1=1…1^2=1\)
Others are \(5^1=5….5^2=25\) and \(6^1=6……6^2=36\)
Hence, possible answers - 0, 1, 5 and 6.
Insufficient
Combined
Answer is 1.
Sufficient
C
