number system Model Questions & Answers, Practice Test for ssc mts paper 1 2023
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How many natural numbers are there which give a remainder of 41 after dividing 1997?
Answer: (a)
Let us assume that the quotient is Q and divisor is D.
Using the condition given in question, 1997
= QD + 41 ⇒ QD = 1956.
Now we will factorize 1956 in two parts such that D (divisor) is more than 41.
An amount of Rs.123098 is distributed equally amongst 61 persons. How much amount would each person get?
Answer: (c)
Amount received by each person
= $123098/61$ = Rs.2018
What is $26^2 + 97^2$ equal to ?
Answer: (d)
Here we can check the unit digit
Unit digit of $26^2 + 97^2$ = 6 + 9 ⇒ 5
Now according to option
Unit digit of $79^2 + 62^2$ = 1 + 4 ⇒ 5
So, $26^2 + 97^2 = 79^2 + 62^2$
The numbers 1 to 29 are written side by side as follows 1234567891011............................ 28 29 If the number is divided by 9, then what is the remainder?
Answer: (c)
Sum of the digits of the 'super' number
= 1 + 2 + 3 + ................... + 29
= $29/2$ .{2 × 1 + (29 -1).1}
= $29/2 . (2 + 28) = {29 × 30}/2 = 29 × 15 = 435$
Now, sum of digits in the number 435 = 4 + 3 + 5 = 12 which gives a remainder of 3 when divided by 9.
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of $(1/x - 1)(1/y - 1)(1/z - 1)$ is
Answer: (b)
The value of the expression will be least when x = y = z = 1/3.
Hence, the least value = $(1/{1/3} - 1)^3$
= 2 × 2 × 2 = 8.
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