Guess & Check Questions come in many
forms. The type I’m discussing here involves 2 items, the total of which is
given. The 2 items have different values (cost, amount etc), the total of which
is also given.
In Example 1 below, there are 30 apples and
pears which cost $10.
How to do this type of Guess & Check
questions:
- Draw a table with 7 columns, 2 each for each item, 1 for the Total and 1 for Checking
- Write 1 and 2 in the first two rows of 1 of the items, then calculate everything else in the first two rows.
- From the table, calculate the increase or decrease in the Total Value (or Cost etc). From this, you know the change in the total for each step.
- Calculate the increase or decrease in the Total Value to reach the Target. Be sure to consider whether this increase or decrease makes sense.
- Divide the Total Change by the Change per Step. You get the number of steps needed to reach the Target.
- Add or Subtract the number of steps to the number of each item. Then complete the whole table.
It’s easier than it looks, but you need to
practise many times until you get familiar with the steps.
Look at my examples.
Example1:
Ali paid $10 for 30 apples and pears. Each apple cost 30 cents and each pear cost 50 cents. How many apples did he buy?
1480 – 1460 = 20 (How much Total decreases
per step)Look at my examples.
Example1:
Ali paid $10 for 30 apples and pears. Each apple cost 30 cents and each pear cost 50 cents. How many apples did he buy?
Apples
(30 cents each)
|
Pears
(50 cents each)
|
Total
|
Check
|
|||
No
|
Cost
|
No
|
Cost
|
No
|
Cost
|
|
1
|
30
|
29
|
1450
|
30
|
1480
|
û
|
2
|
60
|
28
|
1400
|
30
|
1460
|
û (-20 per step)
|
25
|
750
|
5
|
250
|
30
|
1000 (Target)
|
ü
|
1460 – 1000 = 460 (Total decrease to reach Target)
460 ÷ 20 = 23 (No of steps
needed to reach Target)
2 + 23 = 25 (No of apples)
28 – 23 = 5 (No of pears)
Ans: 25 apples
Example2:
During a quiz, Bala had to answer 50 questions. For each correct answer, he was awarded 10 marks. For each wrong answer, 4 marks were deducted. If he scored 304 marks, how many questions did he answer correctly?
Right
(10 marks awarded)
|
Wrong
(4 marks deducted)
|
Total
|
Check
|
|||
No
|
Score
|
No
|
Score
|
No
|
Score
|
|
49
|
490
|
1
|
– 4
|
50
|
486
|
û
|
48
|
480
|
2
|
– 8
|
50
|
472
|
û (-14 per step)
|
36
|
360
|
14
|
– 56
|
50
|
1000 (Target)
|
ü
|
486 – 472 = 16 (How much Total decreases
per step)
472 – 304 = 168 (Total decrease to reach Target)
168 ÷ 14 = 12 (No of steps
needed to reach Target)
48 – 12 = 36 (No Right)
2 + 12 = 14 (No Wrong)
Ans: 36 correct answers
Remark:
For this question, if you write 1 and 2 in the Right column, you will end up with a negative Score. If this happens, simply switch to the Wrong column when you write 1 and 2.
GC1:
GC1:
Charles drew 40 triangles and hexagons (6-sided figures). The figures
he had drawn had 159 sides altogether. How many triangles did he draw in all?
GC2:
Don bought 6 packets of sweets. Each packet contained 40 sweets. He
repacked the sweets into bags of 8 or 12. In the end, he had 25 bags in all.
How many bags of 8 did he pack?
GC3:
There are some ducks and cows in a farm. There are a total of 20 heads
and 56 legs. How many ducks and how many cows are there?
GC4:
Mr Ho has 100 shirts.
Some shirts have 5 buttons and the rest have 8 buttons. There are 659 buttons
altogether on the shirts. How many shirts have 8 buttons?
GC5:
There were 35 pupils in a class. The pupils read a total of 266 books in Term 1. The girls read an average of 10 books while the boys read of average of 6 books. How many boys were there in the class.
GC6:
|
|||||||
How many children went to the concert?
GC7:
Peter rears horses and ostriches on his farm. In all, they have 314 eyes and 438 legs. How many horses does he have?
A length of wire is 50 m long. It is cut into 150 pieces that are either 20 cm long or 45 cm long. How many 20‑cm long pieces are there?
|
|||||||
367 people attended a magic show. They paid $5 826 altogether.
How many children were
there?Mr Shane has 405 sheep and chickens on his farm. The sheep and chickens have 1034 legs altogether. How many sheep did he have?
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