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SEVENTH GRADE / MATHEMATICS /INTEGERS TEST 7.1.1.3

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.

 INTEGERS
    ♦ 
Whole numbers are counting numbers (1,2,3,...) with the addition of 0; and integers are these plus the negatives of counting numbers: { ...,-2,-1,0,1,2,...}. Counting numbers are also called natural numbers by the way.
    ♦ Integers are very important because all of our calculations are done via integers. Here we will learn the way of well defining consecutive basic operations and evaluating them.
1. [1:(1-3)- 1/(1+3)]:[1:(-8)] = ?

a) 4
b) 8
c) 5
d) 6
See as quick as possible that (1-3)x(1+3) = -8 (12-32) .
 
2. Which is the correct order among =10100, B=100100 and 100! ?

a) 10100>100!>100100
b) 10100>100!<100100
c) 10100<100!<100100
d) 10100<100!>100100
Each one having 100 factors ...
10100=10x10x10x10x10x10x10x10x10x...x10x10x10x10x10x10x10x10x10 ,
100!=1x2x3x4x5x6x7x8x9x...x92x93x94x95x96x97x98x99x100 and
100100=100x100x100x100x100x100x100xx100x100x...x100x100x100x100x100x100x100xx100x100 .
http://math.stackexchange.com/questions/151588/factorial-vs-power-sequence.
 
3. Which one is nearest to 10! : 1010 ?

a) 1/3000
b) 3000
c) 1000
d) 1/1000
(1x2x3x4x5x6x7x8x9x10):(10x10x10x10x10x10x10x10x10x10)=
(1x2x3x4x5x6x7x8x9):(10x10x10x10x10x10x10x10x10)=
(3x2x5x3x7x4x9):(5x10x10x5x10x5x10x5x10)=
(3x3x7x4x9):(5x10x5x10x5x10x5x10)=
(14x81):(25x125x1000)=1134:3125000=567:1562500 i.e. approximately 57/156250 i.e. approximately 1/3000 ...
 
4. Which result is obtained if the expression on the board is evaluated ?

!


a) 51
b) 30
c) 55
d) 87
7-6+9+(21-24:(1:(1-2)))=10+21-24:(-1)= ... .
 
5. Two 2-digit numbers whose sum is the number seen on the figure are generated by using each digit from the possible 10 only once.
Which is the maximum number this way to be attained ?

!


a) 71
b) 67
c) 44
d) 37
This case is relatively easy. 77-10 is 67 which has no contradiction to any of the conditions given .
 
y
6. Three 2-digit numbers whose sum is 77 are generated by using each digit from the possible 10 only once.
Which is the maximum number this way to be attained ?

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



a) 39
b) 41
c) 34
d) 42


This is bit harder, have please a look at ry1 .
39+10+28= ... .
 
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7. What is the number of generated 3-digits if each digit is restricted (no sign) to be used only once and which one is the greates ?

a) 648 & 987
b) 751 & 987
c) 648 & 989
d) 649 & 997
For hundreds' we have only 9 choices because 0 is not used, ...
 
8. What is the max. number of 2-digit pairs (two 2-digits) generated under restriction of using each digit only once ?

!


a) 2732
b) 4054
c) 3032
d) 4032
For tens' and ones' of the first number we have 9 choices. 72 of them do not use 0 at all.
If 0 is used in the first number of the pair, second will have 8 choices for tens' and 7 for ones'.
If 0 is not used in the first number of the pair, second will have 7 choices for tens' and 7 for ones'.
9x8x7 + 72x7x7 = ?
 
9. What is the number of 2-digit numbers less than 50 if any possible digit is to be used only once in each number ?

a) 26
b) 33
c) 36
d) 45
4x(10-1) = ?
 
10. What is the total number of 2-digit (only digits, no signs) pairs having a sum less then 100 ?

a) 2035
b) 1225
c) 925
d) 1300
The greater may be 89, there is only one pair candidate (10) .
The greater may be 88, there are 2 pair candidate (11 and 10) .
...
The greater may be 50, there are 1, 2, ..., 49 .
50 olabilir. Karşılık 10, 11, ..., 49 vardır.
Sum of all is, after nx(n+1)/2, 49x25=? .
 
11. What is the total number integer pairs having a sum less then 100 ?

!


a) 20
b) 10
c) 100
d) ∞
Consider all negatives .
 
y
12. The total of 3 three-digit numbers in all of which each digit is used at most once is 954. Which of the followings my be the greatest of these numbers in this special case ?

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

RY1 RY2



a) 741
b) 477
c) 615
d) 459
If the greatest of the numbers having all these were to be asked, the question would really be a hard one; now it is enough to check the answers given.
 
13. A,B and C are integers and AxB=12 and BxC=20 are valid. It is further known that B2 is a 2-digit number.
Which is the solution set for AxBxC ?

a) {60}
b) {-60,60}
c) {-30,30}
d) {-30}
AxB2xC=240 .
The squares of the first 5 numbers: 1,4,9,16 and 25 . First 3 are out of context.
25 is not a multiple of 240, in addition ...
 
14. Total of 5 different 3-digit numbers is 581 and one of these numbers is a square number. Which choice may be the greatest of these 5 ?

a) 155
b) 151
c) 321
d) 97


The square number should be 112=121 . The smaller ones are 101, 103 and 105 .
 
15. 3 consecutive integers are known to have equal sum and product. Which is the solution set ?

a) {(-3,-2,-1),(-1,0,1),(1,2,3)}
b) {(-3,-2,-1),(1,2,3)}
c) {(-3,-2,-1),(-1,0,1)}
d) Φ
Let the consecutive 3 be A-1, A vand A+1 .
(A-1)xAx(A+1)=A-1 + A + A+1 i.e. (A-1)x(A+1)=3 i.e. A2-1=3 i.e. a2=4 which means A=-2 or A=2 .
Remember also that the number factored out may be 0 .
A=-2, 0 and 2 .
A-1=-3 , -1 and 1 .
A+1=-1 , 0 and 3 .
 
16. How many of the 5 numbers to be figured out from the figure are prime ?

!


a) 2
b) 4
c) 1
d) 3
. Products can not be prime and 343=350-7.
 
17. What is the minimal AxB value according to data obtained from the figure below ?

!


a) 54
b) 49
c) 61
d) 34
A+B=15 and 1x15 excluded .
 
y
18. What is the minimal possible integer A-B value if A:B = (6+12+18+...+240):(3+6+9+...+120) ?

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


a) -2
b) 1/2
c) 1
d) -1
3x(1+2+3+...+40)=60x41=2460. Have a look at ry1 for additional help .
 
19. What will be the greatest obtainable product if 2 factors of 1000000! are multiplied ?

a) 999 999 000
b) 999 999 000 000
c) 625 999 000 000
d) 625 999 000
1x2x...x999 999x1 000 000 .
 
20. If ones' and hunderds' are exchanged in number ABC, the difference will be 188. What should then C-A be ?

a) 1
b) 4
c) 2
d) 9
If Cx100-Ax100 +Bx10-Bx10+A-C = 100x(C-A)-(C-A) = 188 ... .
 
21. The figure shows how maize silage is obtained. It is used by dairies. Turkey needs about 15 million tonnes of it.
The yield per decare of GDO maize is about 5 tonnes whereas the conventional yield is 1/3 rds of this amount.
How many decares of more land is needed if only conventional maise is cultivated instead of only GDO maize ?

!


a) 1 million
b) 9 million
c) 3 million
d) 6 million
If only GDO maize should be cultivated on 3 million decares .
 
y
22. To which choice will the value of the Nth element of the pattern seen in the figure be very close for great N (1000 and greater)?

!


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

RY1 RY2



a) -2
b) -1
c) 2
d) 1


Try to obtain the formula of the pattern. Look at ry1 if needed .
23. [7+12:(1:3)-16:2x1]:(5+12:1:3-16:2x1)-1 = ?

a) 34
b) 45
c) 54
d) 35
7+12:(1:3)-16:2x1=35 and 5+12:1:3-16:2x1=1.
24. (5+12:1:3-16:2x1)x(5+12:1:3-16:2x1):(1/10)= ?

a) 3
b) 10
c) 9
d) 1/3
5+12:1:3-16:2x1=1 .
25. 9:(7+12:1:3-16:2x1):(7+12:1:3-16:2x1) = ?

a) 1
b) 3
c) 1
d) 9
We repeatedly advice to evaluate the paranthesis at first, because they are to avoid ambiguity. Sometimes there may be some simple operations that are attractive to handle first, but keep rather the sure track. Then, after paranthesis, keep the order "powers-multiplication and divisions-addition and subtractions". In case of equal priorities, not usual because we normally use aranthesis, keep the read/write order (left first).
7+12:1:3-16:2x1=3 .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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