Test: High Order Thinking Skills - 3 - Class 4 MCQ

(i) The difference between the place value and the face value of the digit 9 in 49231:

• Face value of 9: The face value of a digit is the digit itself. For 9 in 49231, the face value is 9.
• Place value of 9: The place value of a digit is determined by its position in the number. Since 9 is in the thousands place, its place value is 9 × 1000 = 9000.
• Difference between place value and face value = 9000 - 9 = 8991.

(ii) Rounding 25432 to the nearest hundreds:

• Last two digits in 25432 are 32. Since 32 is less than 50, we round down, making the number 25400.

So the correct answers are:

• (i) 8991
• (ii) 25400

Thus, Option A is correct: 8999 and 25400.

Clue 1: The sum of all the digits is 24. 

Clue 2: The greatest common divisor (GCD) of 4 and 8 is 4. → So, the digit at the ones place is 4. 

Clue 3: The digit at the hundreds place is the second multiple of the digit at ones place. → Second multiple of 4 is 8. → So, the digit at the hundreds place is 8. 

Clue 4: The greatest 1-digit prime number is 7. → So, the digit at the thousands place is 7.

Now, let’s find the digit at the tens place:
- Sum of known digits: 7 (thousands) + 8 (hundreds) + 4 (ones) = 19 
- Total sum required: 24 
- Therefore, the tens digit = 24 - 19 = 5 
Putting it all together: - Thousands place: 7 - Hundreds place: 8 - Tens place: 5 - Ones place: 4 
The 4-digit number is 7854, which matches option a).

Clue 1: The sum of all its digits is 16.

Let the digits of the 4-digit number be represented as:

• Thousands place = a
• Hundreds place = b
• Tens place = c
• Ones place = d

The sum of the digits is:

a + b + c + d = 16

Clue 2: The digit at ones place is the square root of 16.

The square root of 16 is 4, so:

d = 4

Clue 3: The digit at hundreds place is 2 more than the digit at ones place.

Since d = 4, the digit at the hundreds place will be:

b = 4 + 2 = 6

Clue 4: The digit at thousands place is twice the digit at tens place.

This means:

a = 2 * c

Step-by-Step Solution:

Now, let's use these clues to find the 4-digit number:

a + 6 + c + 4 = 16

Simplifying:

a + c + 10 = 16 → a + c = 6

2c + c = 6 → 3c = 6 → c = 2

a = 2 * c = 2 * 2 = 4

1. The sum of the digits is 16:
2. From Clue 4, we know a = 2c. Substituting this into the equation:
3. Now that we know c = 2, we can find a:

Final Number:

• Thousands place = a = 4
• Hundreds place = b = 6
• Tens place = c = 2
• Ones place = d = 4

So, the 4-digit number is 4624.

Step 1: Represent the Number

The number is of the form: (thousands place) (hundreds place) (tens place) (ones place).

So the number is: (odd prime number) (2 × x) (x) 3.

Step 2: Use the Sum of Digits

The sum of the digits is:

Thousands place + Hundreds place + Tens place + Ones place = 18 (odd prime number) + 2x + x + 3 = 18 Simplify: (odd prime number) + 3x + 3 = 18 (odd prime number) + 3x = 15 (odd prime number) = 15 - 3x

Step 3: Try Different Values for x

If x = 4:

(odd prime number) = 15 - 3(4) = 15 - 12 = 3 The thousands place is 3, which is a valid odd prime number.

Thus, the number is: (3) (2 × 4 = 8) (4) (3) = 3843.

Step 4: Verify the Sum

The sum of the digits of 3843 is:

3 + 8 + 4 + 3 = 18

So, the sum is correct.

Answer: D: 3843

Step 1: The digit at thousands place is the smallest odd number. The smallest odd number is 1. So, the thousands place is 1. 
Step 2: The digit at hundreds place is 4 times the digit at thousands place. The digit at hundreds place is 4 × 1 = 4. So, the hundreds place is 4. 
Step 3: The digit at ones place is 2 more than the digit at tens place. Let the digit at tens place be x. Therefore, the digit at ones place is x + 2. 
Step 4: The sum of all the digits is 19. The sum of the digits is: 1 + 4 + x + (x + 2) = 19 Simplifying: 5 + 2x = 19 2x = 14 x = 7 So, the tens place is 7, and the ones place is 7 + 2 = 9. 
Step 5: The 4-Digit Number. The digits are: Thousands place: 1 Hundreds place: 4 Tens place: 7 Ones place: 9 The 4-digit number is 1479. *

Based on the corrected sum of the digits, the correct 4-digit number should be 1479.

• Clue 1: The sum of all the digits is 20. The sum of the known digits 9 (thousands place), 2 (hundreds place), and 5 (ones place) is: 9 + 2 + 5 = 16. To make the total sum 20, the digit at the tens place must be: 20 - 16 = 4.
• Clue 2: The difference between the digits 8 and 3 is 5. So, the digit at the ones place is 5.
• Clue 3: The first even prime number is 2. So, the digit at the hundreds place is 2.
• Clue 4: The greatest single-digit number is 9. So, the digit at the thousands place is 9.

The 4-digit number is 9245.

• Option A: True. The product of two even numbers is always even.
• Option B: True. The sum of two odd numbers is always even.
• Option C: True. A square has four equal sides and four right angles.
• Option D: False. The sum of the angles in a triangle is always 180°, not 200°.
  So, the incorrect option is Option D.

Here, X = 2, Y = 1, Z = 4
So, (Y + Z - X) / 3 = (1 + 4 - 2) / 3 = 3/3 = 1

(i) The difference between the place value and the face value of digit 7 in 57254:

• Face value of 7: The face value is the digit itself, so it is 7.
• Place value of 7: The place value depends on its position in the number. Here, 7 is in the thousands place, so its place value is 7000.
• Difference between the place value and face value: 7000−7=69937000 - 7 = 69937000−7=6993

(ii) The number 20853 when rounded off to the nearest hundreds:

• Look at the tens place digit (5 in 20853). Since it is 5 or greater, round up the hundreds place.
• The number becomes 20900 when rounded to the nearest hundreds.

Final Answer:

(i) 6993

(ii) 20900

The correct option is: B: 6993, 20900.