solution to question paper 1 --- IPM STD 5

What is the sum of the number in the series 3, 7, 11, 15, ...., 75

Answer:

I am attaching a small explanation. in case you are interested to know why we are doing whatever we are doing in the way it is done.

We find that each number differs from the other by 4. We will note this difference as “d”

Now say, the middle number of this series is “a”.

So there are as many numbers before the middle number as there are after.

......( a – 4d), (a – 3d), (a – 2d), (a – d), a, (a + d), (a + 2d), (a + 3d), (a + 4d) ........

Sum of all this numbers = S

= ......( a – 4d) + (a – 3d) + (a – 2d) + (a – d) + a +(a + d) + (a + 2d) + (a + 3d) +(a + 4d) ........

We will find that the –d terms will cancel out with +d terms on the other side of “a”

So, S= na, where the “n” = total number of terms.

But we still can’t solve the problem, because we do not know the value of “a” and we do not know “n”.

Let us see if we can find “a”.

We know the first term as say t1 = a – (n/2)d and the last terms as tn = a + (n/2)d

Adding the first and the last term we find t1 + tn = a –(n/2)d  + a + (n/2)d = 2a

So, a = (t1 + tn)/2

Also, tn = t1 + (n-1)d

Or n = ^{(tn – t1)}/_d + 1

Answer: 

The question now becomes simple

 We have,  a = (t1 + tn)/2   = (3 + 75)/ 2 = 39

And, n = ^{(tn – t1)}/_d + 1  = (75 – 3)/ 4 + 1 = ( 72/4) + 1 = 19

So, S = na = 19 x 39 = 741

solution question paper 1 -- IPM STD V

A number leaves a remainder of 26 when divided by 357. What will be the remainder if the same number is divided by 17?

Answer:

Please remember this question has a solution only if 357 is completely divisible by 17.

Check: 357 / 17  = 21

So, 26 / 21 = 1 ⁵/₂₁. The remainder is 5.

solution to question paper 1 - IPM STD V

The least number to be multiplied by 17640 so that the result becomes a perfect square is -------------

Answer:

17640 = 3 x 3 x 2 x 2 x 7 x 7 x 2 x 5

So, the least that should be multiplied = 2 x 5 = 10 to make it a perfect square.

solution question paper 1 -- IPM STD V

A number leaves a remainder of 83 when divided by 123. What will be the remainder if the same number is divided by 41?

Answer:

Please remember this question has a solution only if 123 is completely divisible by 41.

Check: 123/41 = 3

So, 83 / 41 = 2 ¹/₄₁. The remainder is 1.

answer to question paper 1------- IPM STD 5

In a test there are 50 questions. A student gets 5 marks for the right answer and 1 mark is deducted for every wrong answer. If she attempted all the questions and got 78% marks, how many questions did she attempt correctly?

IPM STD V questions paper 1

In a test there are 50 questions. A student gets 5 marks for the right answer and 1 mark is deducted for every wrong answer. If she attempted all the questions and got 78% marks, how many questions did she attempt correctly?

A number leaves a remainder of 83 when divided by 123. What will be the remainder if the same number is divided by 41?

The least number to be multiplied by 17640 so that the result becomes a perfect square is --------------

A number leaves a remainder of 26 when divided by 357. What will be the remainder if the same number is divided by 17?

What is the sum of the number in the series 3, 7, 11, 15, ...., 75

How many numbers between 281 and 651 are divisible by 2,3,4, and 5?

If two fifth of one fourth of a number is 4, what is the sum of the digits of the number?

A number when divided by 5 diminishes by 40. What is  the number?

The sum of 3 consecutive even number is 78. What is the middle number?

Nanu was asked to divide a number by 4, instead she multiplied it by 4. Her answer was 60 more than the correct answer. What was the number?

The average age of A and B is 18. If C is 9 years old, what is the average age of A,B and C?

The average age of 5 children is 8 years. If the father’s age is also included then the average age of the group becomes 13 years. What is the age of the father?

The average of three numbers is 135. The largest number is 180 and the difference between the other two numbers is 45. What is the smallest number?

The average of 13 observations is 23. The average of the first 7 observation is 27 and the average of the last 7 observation is 24. What is the value of the seventh observation?

5 years ago the average age of a family of 3 members was 17 years. A baby girl was born during the same period such that the average age of the family remains unchanged? What is the age of the baby now?

The average marks of 30 students in the class are increased by 1.2 when a student of mark 42 is replaced by another student. What was the mark obtained by this new student?

divisibility - IPM V

What is the least valve of K such that 4876k is divisible by 11.


Answer:

k + 7 + 4  = 11 + k
8 + 6 = 14
therefore, 14 = 11 + k
or, k = 3.

simple equations IPM STD V

2/3 of the committee members are females. 1/4 of the male members are married. If there are 9 unmarried male members in the committee, then how many members are there in the committee?

number, LCM and divisibility -- IPM STD V

Find the number of integers between 200 and 600 divisible by 2,3 and 7?


Answer:

if a number is divisible by 2,3 and 7, it must be divisible by the LCM of the three numbers.
LCM of 2, 3, and 7 is 42.

42 have 4 multiples in 200 (i.e. ²⁰⁰/ ₄₂ = 4 ³²/₄₂)
And 42 have 14 multiples in 600 (i.e. 600/42 = 14 ¹²/₄₂)
So, number of integers between 200 and 600 that is divisible by 42 = 14 – 4 = 10.
Answer.