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FIFTH GRADE /NATURAL NUMBERS / TEST 1.3

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

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

  
 NATURAL NUMBERS,

  WE TAKE THE COUNTING NUMBERS 1, 2, 3, ... 

 ♦  SOMETIMES WE ADD 0 TO THEM and WE GET THE NATURAL NUMBERS

IN OTHER WORDS THE NATURAL NUMBERS ARE
THE NUMBERS (0), 1, 2, 3, 4, ...

  0 BEING NOT NECESSARYLY INCLUDED.
1. The ages of a modern couple are 2-digit numbers. The age of the man is the same as his wife's age with the digits reversed and 9 greater than the age of the wife. How old should the woman be if the digit sum of woman's age is 7 ?

!
a) 45
b) 54
c) 34
d) 43
Let the age of the man be AB. From 10xA + B = 10xB + A + 9 we see that A - B = 1 i.e. the digits must have a difference of 1 .
There are two unkowns and two given facts. One we used and found A - B = 1. The choices are than 23, 34, etc. ... for the woman's age. Only 1 of them satisfies digit sum of 7 .
Of course the equations A-B=1 and A+B=7 may be solved by obtaining 2xA=8 from summation of both sides. .
2. In the five-digit number A6A40, each of the "A"s represents the same digit and A6A40 is divisible by 8. What digits may A represent ?

a) 0, 2, 4, 6, 8
b) 2, 4, 6, 8
c) 4, 6, 8
d) 6, 8
Because thousands are divisible by eight, this divisibility (by eight) is valid if and only if the number formed by the last 3 digits is divisible by 8 .
Be careful about 0; it can not be the first digit .
3. Let us assume that the old Babylonians used the following codes as they express the angles in base 60 as minutes, seconds and split-seconds.

!

If they also wrote from left to right as we do, which choice would give their code for 10'
15 '' 23 ''' ?

!


a) I
b) III
c) II
d) IV
In the table given, A corresponds to 10 .
4. How would the old Babylonians express an angle of 43° 22'' 37''' ?

!


a) IV
b) III
c) I
d) II
... corresponds to 43 .
5. Which of the following choices gives us a babylonian 3-digit number in our lovely base 10 ?

a) K1x360 + K2x60 + K3
b) K2x3600 + K1x60 + K0
c) K1x3600 + K2x60 + K3x10
d) K2x3600 + K1x60 + K010
Babylonian place values are assumed to be 1 , 60, 60x60=3600, 60x3600=216000 ... .
y
6. What would correspond to 27 in base 16 in our base ten ?


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 39
b) 29
c) 36
d) 45
Use windows calculator's programmer menu if you desire so .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Let N be a number that divides 155 with a remainder of 5. Which of the followings does not belong to (the set of) numbers that N can be(long to). ?

a) 2, 3 and 5
b) 10 and 15
c) 10, 15 and 30
d) 15, 30 and 50
155-5=150. 150 is divisible by 2, 3 and 5 but ... .
Other divisors 6, 10, 15, ... .
8. Let all the odd numbers from 1 through 309 inclusive be written. How many times will the digit 0 appear ?

!
a) 44
b) 25
c) 12
d) 15
Be careful, odd numbers do rarely contain 0 .
9. Dr. A. Bilgin Karabasan is a marine biologist marking anchovies (hamsi), horse mackerels (istavrit), gray mullets (kefal), and gobies (kaya balığı) found in the Black Sea.

1. On the first day he marked 12 anchovies , 10 horse mackerels , 12 gray mullets , and 14 gobies .
2. The second day he marked 10 anchovies , 14 horse mackerels, 14 gray mullets, and 12 gobies .
3. The third day he marked 12 anchovies , 14 horse mackerels, 14 gray mullets, and 12 gobies .
4. The fourth day he marked 12 anchovies , 16 horse mackerels, 12 gray mullets, and 14 gobies .
5. The fifth day he marked 20 anchovies , 12 horse mackerels, 12 gray mullets, and 12 gobies .

If he continues to spot the animals at the same rates, on what day will he spot 74 animals ?

!
a) 17th
b) 9th
c) 12th
d) 14th
There seems to be an arithmetic increase of 2 animals per day . The first day he marked 48 animals.
The fourth day he marked 54 animals is to be noted. This makes calculation easier.
10. The sum of two natural numbers is 32. What are the numbers if the larger number divided by the smaller number gives the quotient 5 and the remainder 2 ?

a) 32 and 4
b) 27 and 5
c) 25 and 7
d) 29 and 3
Let the dividend be A and divisor B. Then A = 5xB + 2 and A+B = 32 => A = 32-B. Then
30-B = 5xB and of course 6xB = 30
11. Satyaki's age is the same as his grandfather's with the digits reversed. The product of their ages gives the year Gen. Eisenhower took command of Allied Invasion Force in London.
How old may Satyaki and his grandfather be?

!


a) 26 and 62
b) 28 and 82
c) 27 and 72
d) 19 and 85
The date should be between 1940 and 1945. 27x72 = 1944 .
y
12. 12 means 1 x 1, 22 means 2 x 2, 32 means 3 x 3, and so forth.
Find the value of A if A = 22+ 42+ 62 + 82 + ... + 102 .


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2

a) 220
b) 330
c) 150
d) 350
You can of course make a term by term calculation but have please a look at ry1 .
13. Which of the following statements are true ?

I: In this coding of the Blacksheep Tribe it is easy to continue coding as the numbers increase.
II:
In this coding of the Blacksheep Tribe it is easy to perform the summation and subtraction.
III:
In this coding of the Blacksheep Tribe it is easy to perform the multiplication and division.
IV: Considering our mental abilities and the 4 basic operations, base 10 coding is a very convenient coding.


a) I , II and III
b) I , III and IV
c) I , II and IV
d) II , III and IV
Codings in which summation and subtraction is easy/less needed make multiplication and division harder.
14. What is the difference of place and digital values of 7 in the decimal number 3 656 786 ?

a) 7000
b) 693
c) 700
d) 7004
There is only a 7 in the units period (http://www.math.com/school/subject1/lessons/S1U1L1DP.html) .
15. The upper display increases 3 by 3 and the lower decreases 6 by 6 per second.
How many second should elapse till they show the same values ?

!
a) 36
b) 38
c) 42
d) 46
What is obtained if the difference is divided by 9 ?
16. Which of the following statements are false ?

I : 3 , 30 , 6 , 60 , 9 , 90 , ... is a nested pattern.
II : 7 , 14 , 21 , 28 , 42 , ... is a pattern with improper term(s).
III : 9 , 18 , 27 , 35 , 45 , ... is a pattern with failing term(s).
IV : Patterns are not necessarily be finite.

a) All
b) II and III
c) I and II
d) III and IV
Nested pattern if two paterns each having its own rule are embedded (like I) .
17. Which resulting pattern will be obtained if P1 = 7 , 21 , 35 , 49 , ... are P2 = 7 , 14 , 21 , 28 , 35 , ... (term by term) subtracted ?

a) 0 , 7 , 14 , 21 , ...
b) 7 , 14 , 21 , 28 , ...
c) 0 , 14 , 21 , 28 , ...
d) 0 , 7 , 14 , 28 , ...
(Term by term subtraction/addition of patterns may end up with another one .
y
18. A prime number is a number that is only divisible by 1 and itself (being different from 1). In the figure below you see an algorithm that separates primes and non primes.
How many different colors should the elipses/circles in the figure have ?


!

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1
RY2



a) 5
b) 2
c) 4
d) 7


Having a look at ry1 will certainly be useful.
19. Sum of eleven consecutive multiples of 3 is known to be 44 022. What should be the average of these numbers ?

a) 4000
b) 4020
c) 4002
d) 4011
Just divide the sum by 11.
20. What should be the value of A, if A5 x A7 = 1295 where A is a digit at tens'place ?

a) 6
b) 9
c) 4
d) 3
A can not be greater than 4 because 40 x 40 is 1600 .
21. How many natural numbers can be formed by using only the digits 5, 4 and 0 only once (within the formed number) ?

a) 4
b) 6
c) 9
d) 18
0 is not a valid choice for hundreds' .
y
22. Istanbul is a metropol and a good deal of transportation possibilities exist. Akbil is a method of payment (formerly) a single length distance costs 1.65 T.L. while a double length costs 3.3 T.L. and a transfer within two hours costs 0.85 T.L.
The reduced rates for students etc. is for single length distances 1.1 T.L. and transfer costs 0.45 T.L.
Under these conditions the total fare of any two persons at any time of the day can not be ... T.L.


!

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 3.95
b) 4.85
c) 4.08
d) 4.65
Any sum of the numbers given must have a 0 or a 5 at the end .
23. When I open my Science book, two pages face me and the sum of the two page numbers is 445. What is the number of the next odd numbered page ?

!

a)
b) 225
c)
d)
The open pages should be consecutive with page numbers 222 and 223
24. Which of the following statements is not true ?

a) Large code tables require more to memorize .
b) There is nothing useful in using large code tables.
c) Large code tables repel the student.
d) Base 60 has a multiplication table with 1770 elements .
The number of elements of base 10 multiplication table = (81-9)/2 + 9 = 45 .
25. Which of the following statements is/are wrong ?

I : 10700 > 100100
II : 1 quadrillion is the greatest natural number .
III : 300045 is three hundred thousands and fourty-five.
IV : To each natural number we can add 1.
a) All
b) III and IV
c) I and II
d) I, III and IV
There is no greatest natural number .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
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