Sample Questions

Sample Questions:

• The numbers when we count by 10 are 10, 20, 30, 40, 50, 60.

If you add 30 to the number, it’s still less than 60. So 30, 40, 50, 60 cannot be the number.

That leaves us with 10 and 20.

Our number is greater than 10 therefore answer is 20

• Let’s prove this with a counter example.

Let our numbers be m and n where n = 1

Product of the two numbers is m × n = m × 1 = m

Sum of the two numbers is m + n = m + 1

And m + 1 > m hence in this case sum of the two numbers is greater than their Product making above statement false

• Let the size of the sunflower be x on Monday.

We know size doubles everyday – let’s make a table

Day Size
Monday x
Tuesday 2x
Wednesday 4x
Thursday 8x
Friday 16x
Saturday 32x

How much bigger is the sunflower on Saturday compared to Monday = 32x ÷ x = 32.

Hence sunflower is 32 times bigger on Saturday than on Monday

• We will use guess and check strategy and systematically explore the combinations

Boys in the family Girls in the family Brothers boy has(A) Sisters boy has(B) Brothers girl has (C) Sisters girl has (D) Answer: We want Col A = Col B AND Col C = 2 × Col D
1 1 0 1 1 0 Boy does not have as many brothers as sisters
2 1 1 1 2 0 Boy has as many brothers as sisters but sister does not have half as many sisters as brothers
2 2 1 2 2 1 Boy does not have as many brothers as sisters
3 2 2 2 3 1 Boy has as many brothers as sisters but sister does not have half as many sisters as brothers
4 3 3 3 4 2 This combination works. Boy has 3 brothers and sisters. Sister has 4 brothers and 2 sisters.

• Let’s look at any 6 consecutive integers -> 3, 4, 5, 6, 7, 8 or 21, 22, 23, 24, 25, 26.

Notice we will always have a number with 5 in the units digit for any 6 consecutive integers.

Also notice that there will always be at least one even number in the 6 consecutive integers.

5 multiplied by an even number results in a number with a 0 in the units digit.

Thus any six consecutive integers when multiplied with always end with a 0.

• This is a very deceptive problem. Our first instinct is to think that hammer is \$1 and nail is \$0.10. But that is not correct, since the hammer costs a dollar more than the nail and our solution does not satisfy that criteria.

We can solve this problem in two ways

Strategy 1:

Guess and Check

Total Cost Hammer Nail Hammer-Nail Comments
1.10 1 10 0.90 Hammer is not \$1 more than nail. This indicates we need to make the hammer more expensive and/or nail cheaper
1.10 1.05 0.05 1.00 This solution works – Hammer is a dollar more than the nail.

Algebraic Solution

Let h be the cost of the hammer

And n be the cost of the nail.

h + n = 1.10

h –n = 1.00

Adding the two equations.

2h = 2.10

h = 1.05

Substituting in the equations above

1.05 + n = 1.10

n = 0.05