Grade 6 Canadian Math Kangaroo Contest Sample Paper

ID : ca-6-Kangaroo [1]

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Answer Answer t he quest ions ions (1)

Brian Brian remem remembers bers t hat his mot her's birthday is af ter 6 th but befo re 13th of November. His sister Sandra remem remembers bers t hat her mother's birthday is is bef or e 15th and af ter 11th of o f November. November. On which date of November is their mother's borthday ?

(2)

Ruth is cons truct ing a buildin building. g. She finishes

1 8

of the construction construction in 7

1

weeks. How many

2

days in tot al will will she f inish inish co nst ructing the building? building? (3)

What What f raction raction o f f ollowing ollowing letters can be drawn drawn using only straight straight lines ? SWGDQIHEZUB

(4 )

Two walls of an auditorium have to be painted. The first wall is of length 12 meters and height 12 meters. meters. The cost of the paint f or this wall wall is $20 per square square meter. meter. T he second wall wall is of length length 20 meters meters and height height 6 meters. T he cost of the paint paint f or this wall wall is $30 per square square meters. What What is the ratio of the cost s o f painting painting the f irst wall wall to t he second second o ne?

Jo s eph and a nd Sharo Shar o n are in rat io 3:5 . If sum su m of t heir ages a ges is 4 8 years, year s, what is t he age ag e o f (5) Ages o f Jos Sharon ? (6 )

Kim Kimberly can can f inish inish a work in 126 minutes. Do Do nna works twice as f ast as Kim Kimberly. berly. How How lo ng will will it take to finish the work, if Kimberly and Donna work together?

Choose correct answer(s) from given choice (7 )

If you write do wn all all the numbers numbers f rom 1 to 188 (includi (including ng 1 and 188), how many many digits digits would you have writt writt en down?

(8)

(9 )

a. 450 4 50

b. 465 4 65

c. 456 4 56

d. 451 4 51

How many many lines lines o f symmetry symmetry are t here in a rectangle ? a. 2

b. 3

c. 4

d. 1

Kevi Kevin n is the brot her of the so n of Antho Antho ny's ny's s on. How How is Kevin Kevin related related to Antho ny ? a. Son So n

b. Nephew

c. Grandso Grandso n

d. Brother

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(10) The table shows description description of f our Scanne Scanners. rs. P ri rint e r

S p e ci cif ic icat io io n

Scanner Scanner 1 Scans Scans 24 2 pages per minute minute Scanner Scanner 2 Scans Scans 24 0 pages per minute minute Scanne Scannerr 3 Scans Scans 1 page every every 4 s econds Scanne Scannerr 4 Scans Scans 4 pages pages per second

Whic Which h is the fas test ? a. Scanner 4

b. Scanner 3

c. Scanner 2

d. Scanner 1

duct o f two digit number number is is 1924. IfIf the product o f their units units digit digit is 14 and their their tens (11) The pro duct digits digits is 15, then t he numbers numbers are a. 33, 52

b. 55, 37

c. 52, 37

d. 57, 32

(12)

-

= 400 grams grams

-

= 200 grams grams

If the to tal weight weight of

,

and

is 2500 grams, grams, what what is the weigh weightt of

? a. 1300 grams

b. 1100 grams

c. 900 grams

d. 1200 grams

(13) Which Which is is t he next f igure in in the sequence sho wn below? below?

b. a.

c.


d.



(14) If Michael Michael writes all the numbers f ro m 3 to 54, 54 , which which are divisible by 3. What will be the th e number at

13th pos ition? ition? a. 33

4 5 b. 45

c. 39

4 2 d. 42

Fill in the blanks (15)

If AB and CD are parallel, X =

°

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Answers (1)

12th Step 1

Since Since Brian Brian remem remembers bers t hat his mot her's birthdays is af ter 6 th November November and bef ore 13 th November, November, the only pos sible dates are, 7 th November , 8 th November , 9 th November , 10 th November , 11 th November , 12 th November Step 2

Sim Similarly ilarly Sandra Sandra remembers remembers t hat her mot her's birthdays is af ter 11 th November and before 15th November, November, the only pos sible dates are, 12th November , 13 th November , 14 th November Step 3

Now we can can see that 12th November is the common date, therefore their mother's birthdays is on 12 th November.

(2)

4 20 Step 1

We know know t hat, 1 week = 7 days. Theref ore, the number number of days days in 7

=

15

1 2

weeks weeks = 7

1

× 7 days

2

× 7 days

2 =

105

days.

2 Step 2

1

of t he construction is f inished inished in

8

105

days.

2 105 2

Theref ore, the to tal construction will will be finished in in =

days 1 8

=

105

×

2

8

days

1

= 4 20 days. days.




(3)

5 11 Step 1

We have have been given given the f ollowing letters : S W G D Q I H E Z U B. We have have been been asked asked to f ind the f raction raction o f letters f rom these lett lett ers that can be draw drawn n using only straight lines. Step 2

Let us co unt the t ot al num number of letters given given to us. It is 11. Step 3

We can can see that out of the given given 11 lett lett ers, only the f ollowing ollowing 5 letters can be drawn drawn using only straight lines: E H I W Z. None of these 5 letters have any curves. curves. Step 4

Fraction raction o f the letters that can be be drawn drawn using only straight straight lines lines = Number Number of letters that can be drawn drawn using only st raight lines lines To tal num number of letters =

5 11

Step 5

Hence,

5

is the f raction raction of letters letters o ut o f the give given n set o f letters letters t hat can can be draw drawn n

11 using only straight lines.




(4 )

4 :5 Step 1

The length of f irst wall wall = 12 meters meters The height height o f f irst wall wall = 12 meters meters The area of f irst wall wall = length length of f irst wall wall × height height of f irst wall wall = 12 × 12 m2 Step 2

The cos t o f the paint paint f or f irst wall wall is is $20 per square square meter. meter. Theref ore t he cos cos t o f painting painting the first wall wall = $20 × 12 × 12 Step 3

The length of second wall wall = 20 meters meters The height of second wall wall = 6 meters meters The area of second wall wall = length length of second wall wall × height height o f second wall wall = 20 × 6 m2 Step 4

The cos t o f the paint paint f or s econd wall wall is $30 per per square meter. Theref ore t he cost of painting painting the second wall wall = $30 × 20 × 6 Step 5

The f raction raction of the cost cost s o f paintin painting g the first wall wall to t he second second one =

$20 × 12 × 12

=

$30 × 20 × 6 4 5 Step 6

Therefo re the ratio ratio o f the costs of paintin painting g the f irst irst wall wall to the second one = 4:5 4:5




(5)

30 years Step 1

If you loo k at the question caref ully, ully, you you will will notice that the ratio of Joseph and Sharon Sharon ages is 3:5. 3:5. Step 2

Lets the age of Joseph is 3x, then the age of Sharon Sharon is 5x. Step 3

Since Since the sum of thier ages ages is 48 years, theref ore 3x + 5x = 48 8x = 48 x=

48 8

x=6 Step 4

Theref ore the age of Sharon Sharon is = 5x 5x = 5 × 6 [Put x = 6] = 30 years.

(6 )

42 minutes Step 1

If you lo ok at the ques tio n caref ully, ully, yo yo u will will notice that Kim Kimberly can can f inish inish a wo rk in 126 minutes. Step 2

Since Since Do Do nna works twice as f ast as Kimberly Kimberly,, theref ore Do nna can f inish inish a work in one 2 nd time of Kim Kimberly. Step 3

Theref ore a wo rk can can be f inished inished by Donna =

126

minutes

2 Step 4

If Kim Kimberly and Donna work to gether, then bo th o f them can can f inish inish a work in one 3 rd time of Kimberly. Step 5

Now a wo rk can be f inished by Kim Kimberly and Donna =

126

= 42 minutes. inutes.

3




(7 )

c. 456 4 56 Step 1

We need need to f ind the tot al num number of digits digits in all numbers numbers f rom 1 to 188. Step 2

T he range of numbers numbers f ro m 1 to 188 can be broken into numbers with 1, 2 and 3 digits digits respectively: 1-digit numbers: numbers:

1 to 9: A tot al of 9 - 1 + 1 = 9 numbers. numbers. Number Number of digits digits = 9 × 1 = 9 2-digit numbers: numbers:

10 to 99: A tot al of 99 - 10 + 1 = 90 numbers. numbers. Number Number of digits digits = 90 × 2 = 180 3-digit numbers: numbers:

100 to 188: A to tal of 188 - 100 + 1 numbers numbers = 89 numbers. Number Number of digits digits = 89 × 3 = 267 Step 3

To tal number number of digits digits = Number Number of digits digits f rom 1-digit 1-digit numbers numbers + Number Number of digits digits f rom 2digit digit numbers + Number Number of digits digits f rom 3-digit numbers numbers = 9 + 180 + 267 = 456 Step 4

Thus, the number of digits we would have written if we wrote down all the numbers from 1 to 188 is is 4 56 .




( 8)

a. 2 Step 1

Following picture picture sho ws a rectangle

Step 2

Now we can can see that this picture is s ymm ymmetric along vertical and horizo ntal bisecto rs

Step 3

Theref ore rectangle rectangle has 2 lines lines o f symm symmetry

(9 )

c. Grandso Grandso n Step 1

It is given given that, Kevi Kevin n is the brother of the so n of Antho Antho ny's ny's so n.

Step 2

From above chart we can see t hat Kevin Kevin is grandso n of Anthony.




(10 ) d. Scanner 1 Step 1

From the given table we observe t hat t he scanner 1 scans 24 2 pages per minute. minute. Step 2

Scanner Scanner 2 scans 240 pages per minute. minute. Step 3

Scanner Scanner 3 scans 1 page every 4 s econds. So So it scans

1

pages pages in in one second. second. To f ind

4 the number of pages it scans in o ne minute, minute, we need to multiply it with 60. Hence Hence

1

× 60

4 = 15. This means it can s can 15 pages per minute. minute. Step 4

Scanner Scanner 4 s cans 4 pages in one seco nd. Hence Hence to f ind the number number of pages it can scan in one minute we need to multiply it with 60, which which comes comes o ut t o be 4 × 60 = 240 pages per minute. Step 5

From above steps we conclude conclude that s canner canner 1 is f astest .

(11) c. 52, 37 Step 1

Lets ass ume ume two digit digit numbers are, 10x1 + y1 and 10x2 + y2 Step 2

It is given given that t he product o f their units units digit digit is 14 and their tens digits digits is 15, theref theref ore x1 × x2 = 15 -- -- -(1) y1 × y2 y2 = 14 -- -- -(2) and the product of two digit number number is is 1924, (10x1 (10x1 + y1) (10x2 (10x2 + y2) = 1924 1924 - -- -- (3) Step 3

Now we notice that t here are f our variables and only three equations are s pecif pecif ied. We know that f our variables variables cannot cannot be uniqual uniqualy y determine determined d f rom three equations, theref ore lets check check whic which h opt ion sat isf y above three equations. equations. Step 4

If you loo k at the o ption 52, 37, you will will not not ice ice that t he product of their units units digit digit is 14 , the product of their tens digits digits is 15 and the pro duct of two digit digit number i.i.e 52 × 37 = 1924 Step 5

Since Since 52, 52, 37 s atisf ies the all three equations, equations, theref ore we can say that t he numbers numbers are 52, 37.



ID : ca-6-Kangaroo ca-6- Kangaroo [11]

(12) b. 1100 grams Step 1

Let us ass ume, ume,

= A,

= B,

and

=C

Step 2

According Acco rding t o t he ques qu estt ion, io n, B - A = 4 00 gr ams, and an d C - B = 200 20 0 grams, gr ams, and an d A + B + C = 2500 2 500 grams. Step 3

Since Since B - A = 400, we can say that A = B - 4 00, and since C - B = 200, we we can say that C = B + 200. Step 4

We can replace replace the values o f A and C in in A + B + C = 2500 grams, grams, by t he values values we f ound in st ep 3 as: (B - 4 00) + B + (B + 200) = 2500 Step 5

From step 4 we have: have: B - 4 00 + B + B + 200 = 2500 or, B + B + B - 4 00 + 200 = 2500 o r, B + B + B - 200 = 2500 o r, B + B + B = 2700 Step 6

The weight weight o f three B is is equal to 27 00 grams. grams. Therefo re the wei weight ght of one B =

2700

= 900 grams

3 Step 7

From step 3 we have: C = B + 200 or, C = 900 + 200 = 1100 Step 8

Hence Hence the weight weight o f


is 1100 grams. grams.



(13)

d. Step 1

On not icing icing sequence of images, images, and we can see, - 1s t picture is vertical rectangle rectangle - 2nd picture is t riangle riangle - 3rd picture is horizontal rectangle - 4 th picture is f lipped lipped triangle - 5th picture is vertical rectangle rectangle - 6th picture is t riangle riangle - 7 th picture is horizontal rectangle - 8th picture is f lipped lipped triangle - 9th picture is vertical rectangle rectangle Step 2

So we can see that every alternate image is a rectangle, and it is rotated from horizontal to vertical and vicevice- versa Step 3

Sim Similarly ilarly anot her alternate image image is a triangle, which which is f lipped lipped ho rizo ntally Step 4

Since Since image image bef ore last image image is a ho rizo ntal rectangle next image image sho uld be vertical rectangle

(14 ) c. 39 Step 1

Numbers Numbers which are divisible by 3, will be in t he f o rm 1×3, 2×3, 3×3, 3×3, 4 ×3, ...... Step 2

Since Since the numbers numbers st art f rom 3, the number number at 13 th pos ition will be = 13 × 3 = 39.




(15)

21 Step 1

Parallel Parallel line line AB and CD are inters ected by a t ransversal as sho wn below,

Here angle ∠P and ∠Q are co rrespo nding angles. i.e. i.e. ∠P

=

∠Q

Step 2

On comparing given angles with

∠P

and ∠Q,

3x + 2x = 105° ⇒ 5x ⇒ x

= 105°

= 21°



Grade 6 Canadian Math Kangaroo Contest Sample Paper

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