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Number System Basics: Test-5

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Question 1
If p x q x r = +ve where p ,q, r are integer then which of the following statements is correct ?
A
Either q or r must be positive
B
At most two of them is negative
C
At most two of them is positive
D
none
Question 1 Explanation: 
Explanation for (B) – Since at most two of the numbers can be negative, so the no of negative no can be either 0 or 1 or 2. In case of 1 negative no, the answer comes out to be negative
Explanation for (C) – Since at most two of the numbers can be positive, so the no of positive no can be either 0 or 1 or 2. In case of 0 or 2 positive no, the answer comes out to be negative
Options A is self explanatory.so the right answer is option d
Question 2
If P+Q+R= odd  and P,Q,R are integers then which of the following are true
A
Either two of these three numbers must be odd numbers
B
All of them must be odd
C
Either 2 must be even
D
Both 2, and 3 are correct
Question 2 Explanation: 
Since it is given that P + Q + R are odd ,
we have the  following two cases:
Case 1: all of them are odd i.e.= 1+3+5= 9
Case 2: two of them are even = 4+5+6= 15
So the best answer is D, since both the statements are correct
Question 3
Richa has a book which  contains 445 pages but the book did not contain the page numbers, so she decided to write all the page numbers  on the top of the book .Then how many digits  she will use while writing all these page numbers
A
1557
B
1227
C
1478
D
1670
Question 3 Explanation: 
Number of digits from 1 to 9 = 9
Number of digits from 10 to 99 = 90 x 2 = 180
Number of digits from 100 to 445= 346x3= 1038
Hence total number of digits = 1227,
so number of digits that Richa will use are 1227
Question 4
What should be the value of n so that A= 91 +92 +93+ .....................9n is a perfect square?
A
23
B
14
C
25
D
none
Question 4 Explanation: 
The value of A = (9n - 1)}/8 can not be a perfect square by hit and trial.
Question 5
What is the remainder when product of digits of 33333 x 3333366667 is divided by 5?
A
1
B
5
C
6
D
2
Question 5 Explanation: 
The remainder when 33333 is divided by 5 is 3, and 2 when 3333366667 is divided by 5.
So now 3 x 2 = 6 when divided by 5 leaves remainder 1, so the answer is option a
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