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04 May 2019, 08:13
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:25) correct
32%
(01:31)
wrong
based on 162
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What is the tens' digit of a 3-digit positive integer?
(1) The integer is divisible by 9.
(2) The hundreds' digit is 9 times the units' digit.
(1) The integer is divisible by 9.
(2) The hundreds' digit is 9 times the units' digit.
08 May 2019, 10:20
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Hello,
Greetings for the day!
This is a good question which tests you on your knowledge of divisibility rules. It also tests your understanding of the fundamental rules of Data Sufficiency.
A number will be divisible by 9 if the sum of its digits is divisible by 9. For example, 54 is divisible by 9 because the sum of its digits is 9, which IS divisible by 9. On the other hand, 137 is not divisible by 9, because the sum of its digits is 11, which is NOT divisible by 9. Hope this is clear.
Let’s look at the question now.
We can assume the three digit positive integer as xyz. When we do so, it’s clear that we are trying to find the value of y, which is the tens’ digit of the number xyz. Also, note that the biggest value that any of the digits can take is 9, while the smallest value for x is 1 (since it cannot be ZERO) and the corresponding value for y and z is 1.
Let’s analyse the statements now.
Using Statement I alone, we know that integer has to be divisible by 9. This means that the sum of the digits should be divisible by 9, i.e. x + y + z = (Multiple of 9). As can be seen, this equation can be solved in more than one ways.
For example xyz can be 126 or 999 and in both cases, xyz will be a multiple of 9.
Hence, this is insufficient.
Using Statement II alone, we know x= 9z. This can only be satisfied by one set of values viz z=1 and x = 9. However, we do not have any information on the value of y.
For example, the number can be 911 or 921 or 931 and so on till 991.
Hence, this is insufficient.
Combining the data given in both statements, we can conclude the following:
• The number has to start with 9 and end with 1.
• It has to be a multiple of 9. Hence, the sum of the digits has to be a multiple of 9.
Therefore, the only value of ‘y’ that satisfies all the above conditions is 8. So, the number is 981 and hence, the ten’s digit is 8.
This is sufficient.
So, the correct answer option is C.
In a question like this, it is very easy to subconsciously use the data given in Statement I, when trying to solve the question using Statement II alone. So option B is actually a trap answer. So, be very careful when you are analyzing the individual statements.
Hope this helps!
Arvind,
CrackVerbal Prep Team
Greetings for the day!
This is a good question which tests you on your knowledge of divisibility rules. It also tests your understanding of the fundamental rules of Data Sufficiency.
A number will be divisible by 9 if the sum of its digits is divisible by 9. For example, 54 is divisible by 9 because the sum of its digits is 9, which IS divisible by 9. On the other hand, 137 is not divisible by 9, because the sum of its digits is 11, which is NOT divisible by 9. Hope this is clear.
Let’s look at the question now.
We can assume the three digit positive integer as xyz. When we do so, it’s clear that we are trying to find the value of y, which is the tens’ digit of the number xyz. Also, note that the biggest value that any of the digits can take is 9, while the smallest value for x is 1 (since it cannot be ZERO) and the corresponding value for y and z is 1.
Let’s analyse the statements now.
Using Statement I alone, we know that integer has to be divisible by 9. This means that the sum of the digits should be divisible by 9, i.e. x + y + z = (Multiple of 9). As can be seen, this equation can be solved in more than one ways.
For example xyz can be 126 or 999 and in both cases, xyz will be a multiple of 9.
Hence, this is insufficient.
Using Statement II alone, we know x= 9z. This can only be satisfied by one set of values viz z=1 and x = 9. However, we do not have any information on the value of y.
For example, the number can be 911 or 921 or 931 and so on till 991.
Hence, this is insufficient.
Combining the data given in both statements, we can conclude the following:
• The number has to start with 9 and end with 1.
• It has to be a multiple of 9. Hence, the sum of the digits has to be a multiple of 9.
Therefore, the only value of ‘y’ that satisfies all the above conditions is 8. So, the number is 981 and hence, the ten’s digit is 8.
This is sufficient.
So, the correct answer option is C.
In a question like this, it is very easy to subconsciously use the data given in Statement I, when trying to solve the question using Statement II alone. So option B is actually a trap answer. So, be very careful when you are analyzing the individual statements.
Hope this helps!
Arvind,
CrackVerbal Prep Team
28 May 2019, 05:52
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rohan2345
Statement 1:
Consider 3-digit numbers divisible by 9: 333, 999, etc. (Sum of the three digits should equal to a multiple of 9: Divisibility of 9's Rule)
--St. 1 --Not sufficient.
Statement 2:
9_1
The only possible 3 digit number with hundred's digit 9 times of unit's digit.
--St. 2 --Not Sufficient --since the blank can take any digit from 0 to 9.
St. 1+2:
Now, 9_1
has to be a multiple of 9 and therefore, sum of 3-digits must be a multiple of 9 (Rule: Divisibility of 9)
Consider multiples: 9, 18, 27
Since digit has to be b/w 0 and 9 in 9_1
Only sum 18 fits with 8 in tens place.
981
is the number we arrive at.
Option 'C' -- Sufficient together.
