Q1. I am a number. If you count by tens, you will say me. If you add 30 to me, I will still be less than 60. I am not ten. Which number am I?
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
Q2. Is the product of two positive integers always greater than their sum?
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
Q3. A giant sunflower doubles its size every day. How many times bigger is it on Saturday than on Monday?
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
Q4. A boy has as many sisters as brothers. Each sister has only half as many sisters as brothers. How many brothers and sisters are in the family?
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.
Q5. What is the unit digit in the product of 6 consecutive integers?
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.
Q6. A hammer and a nail cost $1.10. The hammer costs a dollar more than the nail. How much does the nail cost?
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
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.
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