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FOURTH GRADE / MATHEMATICS / NATURAL NUMBERS 1.2

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

 In mathematics, natural numbers are

    ♦ 
the ordinary counting numbers 1, 2, 3, ...

    ♦ sometimes zero is also included.


    Ref.-1

    Ref.-2
y
1. The sum of 5 consecutive natural numbers is 265. Which no. is obtained by dividing the greatest by 5 ?

!


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RY2
RY2



a) 10
b) 11
c) 14
d) 55


The figure gives the formula for m consecutive numbers.
Here we have m+1=5 and m=4 .
In this case 265 = (5/2)x(2xn + 4) & 106 = 2xn + 4 & 2n= 102 & n=51 & the gratest of them 51+4 = 55 & 55/15 = 11 .
But this is the formal way to solve; in tests time is scarce. Look at the second tip and ry1 .
As is in ry1, in case we have an odd number of numbers, sum divided buy number gives the midddle term.
2. A photographer demands a definite amount for the first copy and 30 cents less than this amount for every consecutive copy of a definite size.
John John Smith demanded 12 photographs of this size and paid $ 8.70 TL .
What amount is demanded for the first photograph (as cents) ?

a) 50
b) 70
c) 100
d) 110
If it is demanded "k" cents for the first copy, k + 11 x (k-30) cents will be demanded for 12 copies.
Use of trial and error can laso be made:
Since this is a pretty hard nut for 4th graders, trying the easiest to handle choice we get: the first is 100 cents, and 11x70=770 cents for the others .
3. For which 2 consecutive numbers the sum of the first and twice the second gives 212  ?

a) 72 and 70
b) 69 and 70
c) 80 and 81
d) 70 and 71
The sum will not be even for "b".
Numbers in "a" are not consecutive.
Let the first number be n .
The second will be 2 x (n+1) and the sum n + 2x(n+1) = 212 .
In case of trial and error:
"a" and "b" are excluded (the first tip) .
Suppose "c" is true; first no. is 80 and second term of the sum is 2x81=162. Fails.
4. For which 3 consecutive numbers their sum is thrice the minimal of them ?

a) 17, 18 ve 19
b) 24, 25 ve 26
c) 9, 10 ve 11
d) for every
For each natural number n:  n+(n+1)+(n+2) = n+3
5. For which 3 consecutive natural numbers the sum of all is 2 lesser than the least of them ?

a) 1 , 2 and 3
b) none !
c) 2 , 3 and 4
d) 3 , 4 and 5
3xn + 3 = 5xn - 2 i.e. 2xn = 5 must ve valid but can not be for natural numbers !
6. For which 3 consecutive numbers the sum of all three is 3 lesser than 5 times the minimal (the least) of them ?

a) 2 , 3 and 4
b) none !
c) 1 , 2 and 3
d) 3 , 4 and 5
3n + 3 = 5n - 3 i.e. 2xn = 6
7. For which 3 consecutive even numbers the sum of all three is 8 more than twice the least one of them ?

a) 3 , 5 ve 7
b) 0 , 2 ve 4
c) 4 , 6 ve 8
d) 2 , 4 ve 6
y
8. Ali climbs the steps ( floors are not counted as steps) of a five-storey (plus the ground floor ) building between the floors one by one and two by two consecutively. That means, if she sets her foot on each step up to the first floor then she sets her foot on every even numbered step up to the second floor.
Till arriving the fifth floor this way, she has determined that she has set her feet on "n" (a natural number) steps.
Salim, Ali's friend,
- is informed of Ali's style;
- is aware of the fact that there can only be 14, 15 , 16 or 17 steps between the floors
In spite of all his knowns, he could not determine from the number "n" Ali has told him the number of steps between the floors of this particular building.

Which of the followings may be a candidate for "n" ?



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.

RY1 RY2


a) 51
b) 56
c) 49
d) any of the above
Let there be 14 steps between floors; Ali has two possiblities:
a- Beginnin with one-by-one she will set her foot on 14, 7 , 14, 7 and 14 steps between floors consecutively which gives a total of 56 steps.
b- Beginnin with two-by-two she will set her foot on 7, 14, 7, 14 and 7 steps between floors consecutively which gives a total of 49 steps.
Let there be 15 steps between floors; Ali has two possiblities : ...
9. Of which 3 consecutive odd numbers is the sum (of three) equal to twice the greatest of them plus 13 ?

a) 3 , 5 and 7
b) 17 , 19 and 21
c) 15 , 17 and 19
d) 23 , 25 and 27


2xn+1 + 2xn+3 + 2xn+5 = 6xn + 9 = 4xn + 10 + 13 i.e. 2xn + 1 = 23 - 8.
10. A driver takes the distance between Indianapolis and Chicago with a speed of 100 km./hour. Which speed should he keep on the way back to have a round trip average speed of 105 km./hour ?

a) 105
b) 110
c) 120
d) 90
(90 + A)/2 = 85 & A=?
11. Mrs. Transperent has invited her 15 friends to lunch and they all came bringing a total of 15 kids with them. 3750 g. of steak is fried and served, each children having 60 g. less than each adult.
Rounding to the nearest ten, which amount (grams) of steak should each child has eaten ?

a) 100
b) 80
c) 90
d) 150
There are 16 adults including Mrs. Transperent .
For each adult P g. => Px16 + (P-60)x15 = 3750 => 31xP = 4650 .
12. How many times the digit 0 should be used in writing the natural numbers from one up to and including one hundred ?

a) 11
b) 12
c) 9
d) 21
Remember one-o-one, one-o-two, ... etc. .
13. How many times any of the 10 digits should be used in writing the natural numbers from one up to and including one hundred and why do we use roughly 200 digits to write 100 objects down ?

a) 200 , a base is used
b) 197 , base 10 is used
c) 202 , base 10 is used
d) 192 , base 10 is used
14. How many times the digits "1" and the digit "4" should be used in writing the natural numbers from one up to and including one hundred ?

a) 10 and 10
b) 20 and 20
c) 20 and 21
d) 21 and 21
15. The new manager of a building having 100 steps has numerated these steps from the bottom up from 1 to 100 by sticking corresponding digits on each step.
The color of these distinct 1-digit stickers was red for all containig the digit 1 on it and white otherwise.
Afterwords, each step containing a red sticker was colored with red and all of the others were colored with white .
Which of the followings gives the number of white colored steps ?

a) 80
b) 79
c) 77
d) 81
y
16. The new manager of a building having 100 steps has numerated these steps from the bottom up by sticking adhesive digits on each step.
He originally wanted to numerate each step from 1 to 100 in the right order but they could not find a sticker with digit "5" on it. Consequently they skipped 5 and they used "6" instead and continued in ascending order (with 7, 8 etc.)
Which of the followings should be expected to be seen on 100. step ?


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RY1 RY2



a) 121
b) 120
c) 118
d) 125
In this case the coding has base 9 (0 + 8 digits).
The place value of the outermost left digit is 92=81 ,
the place value of the middle digit is 9 and
the place value of the outermost right digit is 1 .
17. The new manager of a building having 100 steps has painted every 10th step with red and all others with white.
How many steps are painted with white ?

a) 69
b) 99
c) 90
d) 93
18. The new manager of a building having 100 steps has hired a painter and called him to paint every 9.th step, i.e, 9th, 18th, 27th etc., with red paint and all the others with white.
The painter has painted the 9th with red and did multiples of this form.
How many steps should eventually be painted with white ?

a) 89
b) 92
c) 88
d) 94
19. Which of the followings are prime numbers ?

a) 0 and 2
b) 1 and 2
c) 2
d) 0 , 1 and 2
prime exactly divisible only by 1 and itself. 1 is not prime by definition.
20. Which is the greatest 3-digit prime number ?

a) 999
b) 997
c) 993
d) 991
21. Which of the followings is wrong ?

a) An even number can not be prime .
b) The no. of primes between 1 and 10 000 are less than the no. of non primes in the same interval.
c) A number having 5 as the last digit can not be prime .
d) 61 is prime .
61 is relly prime.
22. Old Babylonians used base 60. Which choice contains a number which is not a divisor of 60 ?

a) 1 , 5 , 60
b) 6 , 12 , 30 , 60
c) 1 , 2 , 3 , 4 , 5 , 6 , 15
d) 2 , 3 , 4 , 5 , 6 , 8 , 12
60 is not divisible by 8 without remainder.
23. The Holy Quran contains 6666 verses and the average number of verses per page is not a natural number.
What minimal change in the number of pages would make verses per page a natural number ?

a) 33
b) 3
c) 6
d) 66
11x606 = 6666 .
24. 150 students with an average age of 10 were expected to compete in a mathematical competition.
Ten of them having the ages 9 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 11 and 11 could not enter because of different reasons.
What can be said about the avarage age of the students that have taken the test and competed ?

a) 10
b) >10
c) <10
d) 11
25. In a coutry that has 5 cents , 10 cents , 25 cents and 50 cents as coins, Paul has 50 cents and it is known that one of the coins he has is a 25 cent coin.
How many possible combination of coins exist for this case ?

a) 4
b) 2
c) 6
d) 5
One possible combination is 2x25 cents, and another combination may be 25 cents, 10 cents, 10 cents and 5 cents .
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