CBSE Class 7 Mathematics Number Play MCQs Set 11

Answer: (b) taller than the child

Explanation:
1. In this game each child looks only at the children ahead.
2. The child counts how many of them are taller than himself or herself.
3. Children standing behind are never counted.

Teacher's Note:
1. The rule is: count the taller children in front.
2. Children behind do not matter at all.

Answer: (c) whether the number is even or odd

Explanation:
1. Parity is the name for the property of a number being even or odd.
2. An even number can be put fully into pairs; an odd number always leaves one over.

Teacher's Note:
1. Parity has only two values: even or odd.
2. Think of pairing objects to decide it.

Answer: (a) 2n

Explanation:
1. The even numbers are 2, 4, 6, 8, …
2. The number at position n is 2 × n = 2n.
3. The expression 2n − 1 gives the nth odd number instead.

Teacher's Note:
1. Test with n = 3: the 3rd even number is 6 = 2 × 3.
2. 2n − 1 is the matching odd number.

Answer: (d) magic square

Explanation:
1. Such a grid is called a magic square.
2. The common total of every row, column and diagonal is called the magic sum.

Teacher's Note:
1. Remember both terms: magic square and magic sum.
2. Diagonals must also give the same total.

Answer: (b) 55

Explanation:
1. Each number is the sum of the two numbers just before it.
2. So the next number is 21 + 34 = 55.

Teacher's Note:
1. Add the last two numbers to get the next one.
2. Check: 13 + 21 = 34 follows the same rule.

Answer: (c) cryptarithm

Explanation:
1. In a cryptarithm (also called an alphametic) each letter stands for one particular digit.
2. We have to work out which digit each letter stands for.

Teacher's Note:
1. The same letter always means the same digit.
2. We solve it place by place, like a detective.

Answer: (a) Only Statement I is true

Explanation:
1. Two even numbers both pair up fully, so their sum also pairs up: Statement I is true.
2. Two odd numbers each leave one over; the two leftovers make one more pair.
3. So odd + odd is even, and Statement II is false.

Teacher's Note:
1. Try an example: 3 + 5 = 8, which is even.
2. The two leftover dots join to form a pair.

Answer: (c) Both statements are true

Explanation:
1. Nobody ahead of the tallest child can be taller, so the tallest child always says 0.
2. The last child has the most children ahead, which is n − 1.
3. So no child can call out more than n − 1. Both statements are true.

Teacher's Note:
1. A child cannot count more children than are standing ahead.
2. The tallest child always has nobody taller in front.

Answer: (d) A is false, but R is true.

Explanation:
1. Of two consecutive numbers, one is even and one is odd, so R is true.
2. Even + odd = odd, so their sum is always odd (for example 7 + 8 = 15).
3. Hence A is false and R is true.

Teacher's Note:
1. Test A with an example before deciding.
2. Even + odd always gives odd.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A correctly states how the sequence is formed.
2. R is a true historical fact.
3. But who found the numbers and when does not explain how they are formed. So R is not the explanation of A.

Teacher's Note:
1. A historical fact rarely explains a mathematical rule.
2. Ask: does R tell us WHY A happens?

Answer: (d) 33 × 17

Explanation:
1. An m × n grid has m × n small squares.
2. A product is odd only when both numbers are odd.
3. Only 33 × 17 has both numbers odd, so it has an odd number of squares.

Teacher's Note:
1. One even factor makes the product even.
2. No multiplication is needed.

Answer: (a) (i)-(r), (ii)-(q), (iii)-(s), (iv)-(p)

Explanation:
1. The sequence is 1, 2, 3, 5, …, so the 4th number is 5: (i)-(r).
2. The magic sum for 1 to 9 is 15: (ii)-(q).
3. The front child has nobody ahead and says 0: (iii)-(s).
4. 1 + 2 + … + 9 = 45: (iv)-(p).

Teacher's Note:
1. Match the easiest items first.
2. Count the 4th term carefully: 1, 2, 3, 5.

Answer: (c) 5

Explanation:
1. Every line through the centre must add to 15.
2. If 9 were at the centre, the line through 9 and 8 would need 15 − 17 = −2, which is impossible.
3. Checks like this rule out every number except 5.

Teacher's Note:
1. The centre lies on four lines: a row, a column and both diagonals.
2. 5 is also the middle of 1 to 9.

Answer: (b) Virahāṅka

Explanation:
1. Virahāṅka, a Prakrit scholar of about 700 CE, gave the rule in the form of a poem.
2. Pingala lived earlier, Hemachandra later, and Fibonacci wrote about the numbers only in 1202 CE.

Teacher's Note:
1. Link the date 700 CE with Virahāṅka.
2. That is why the numbers carry his name.

Answer: (d) 34

Explanation:
1. Every row, column and diagonal of the Chautīsā Yantra adds up to 34.
2. ‘Chautīs’ means thirty-four, and that gives the square its name.

Teacher's Note:
1. The name itself tells the magic sum.
2. Do not confuse it with 15, the 3 × 3 magic sum.

Answer: (c) ₹196

Explanation:
1. An odd number of ₹1 coins gives an odd amount.
2. An odd number of ₹5 coins also gives an odd amount; the ₹10 coins always give an even amount.
3. Odd + odd + even = even, so the total must be even. Only ₹196 is even.
4. Example: 1 coin of ₹1, 3 coins of ₹5 and 18 coins of ₹10 make 1 + 15 + 180 = ₹196.

Teacher's Note:
1. Find the parity of each heap separately.
2. Then pick the only option with that parity.

Answer: (a) 21

Explanation:
1. Going backwards, each number is the difference of the two after it.
2. 89 − 55 = 34 and 55 − 34 = 21.
3. So two places before 55 stands 21.

Teacher's Note:
1. Subtract to walk backwards along the sequence.
2. Check: 21 + 34 = 55.

Answer: (d) Neither statement is true

Explanation:
1. Even numbers always pair up, so any number of them adds to an even sum. Statement I is false.
2. An even number of odd numbers leaves an even number of extra ones, which pair up again.
3. So that sum is even too, and Statement II is also false.

Teacher's Note:
1. Test with small examples: 2 + 4 + 6 = 12 and 1 + 3 = 4.
2. Both sums are even.

Answer: (b) Only Statement II is true

Explanation:
1. The largest row sum possible is 7 + 8 + 9 = 24, so 25 can never appear. Statement I is false.
2. The smallest row sum possible is 1 + 2 + 3 = 6. Statement II is true.

Teacher's Note:
1. A row holds three different numbers.
2. So every row sum lies between 6 and 24.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The numbers 1 to 9 add up to 45, so the three row sums together make 45.
2. In a magic square the three row sums are equal, so each is 45 ÷ 3 = 15.
3. R gives exactly this reason, so it correctly explains A.

Teacher's Note:
1. Total of all numbers ÷ number of rows = magic sum.
2. Here R is the very working for A.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The parities run odd, even, odd, odd, even, odd, …; the even numbers are at places 2, 5, 8, 11, 14, 17, …
2. 18 is not one of these places, so the 18th number (4181) is odd. A is true.
3. R is also true, but the staircase count does not explain the parity of the 18th number.

Teacher's Note:
1. Even terms come at every third place from the 2nd.
2. R is true but unrelated to A.

Answer: (d) A is false, but R is true.

Explanation:
1. 15 = 1 + 5 + 9 and 15 = 1 + 6 + 8 are the only two ways, so R is true.
2. A corner cell lies on a row, a column and a diagonal, so 1 there would need three such ways.
3. Only two exist, so 1 cannot be in a corner. A is false.

Teacher's Note:
1. Count the lines through a corner: three.
2. Two ways are not enough for three lines.

Answer: (c) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

Explanation:
1. The Lo Shu Square comes from ancient China: (i)-(r).
2. The Chautīsā Yantra is the 10th-century 4 × 4 square at Khajuraho: (ii)-(p).
3. Virahāṅka found the numbers while studying Prakrit poetry around 700 CE: (iii)-(s).
4. Fibonacci wrote about them in Italy in 1202 CE: (iv)-(q).

Teacher's Note:
1. Lo Shu is the oldest recorded magic square.
2. Fibonacci came about 500 years after Virahāṅka.

Answer: (a) 2

Explanation:
1. From the graph, C5 is 132 cm tall.
2. The children ahead of C5 are C1 to C4: 120, 135, 128 and 150 cm.
3. Of these, 135 and 150 are taller than 132, so C5 calls out 2.

Teacher's Note:
1. Look only at the bars to the left of C5.
2. C6 stands behind C5, so it is not counted.

Answer: (c) 7

Explanation:
1. Two two-digit numbers add to at most 198, so D = 1 and the answer is 101.
2. Units: 7 + C ends in 1, so C = 4 with a carry of 1.
3. Tens: B + 7 + 1 = 10, so B = 2. Check: 27 + 74 = 101.
4. B + C + D = 2 + 4 + 1 = 7.

Teacher's Note:
1. Start with the hundreds digit of the answer.
2. Remember the carry in the tens column.

Answer: (a) Only Statement I is true

Explanation:
1. The parities run odd, even, odd, odd, even, odd, …, so every third number from the second is even. Statement I is true.
2. In each group of three numbers only one is even.
3. So there are fewer even numbers than odd ones, and Statement II is false.

Teacher's Note:
1. Write O and E under the first few terms.
2. The pattern O, O, E keeps repeating.

Answer: (c) A is true, but R is false.

Explanation:
1. Doubling every entry doubles every row, column and diagonal total, so A is true.
2. Adding 1 to each of the three numbers in a line raises that line's total by 3, not by 1.
3. So R is false.

Teacher's Note:
1. In a 3 × 3 square each line has three numbers.
2. Adding 1 to each adds 3 to the line total.

Answer: (b) (i)-(p), (ii)-(s), (iii)-(r), (iv)-(q)

Explanation:
1. (i) 38 + 83 = 121, so X = 3: (p).
2. (ii) 83 + 83 = 166, so P = 8: (s).
3. (iii) 56 + 65 = 121, so M = 6: (r).
4. (iv) 5 × 5 = 25, so G = 5: (q).

Teacher's Note:
1. Check each answer by doing the addition.
2. In (iv), 5 × G must end in G.

Answer: (d) 5

Explanation:
1. A row sum of 6 can only be 1 + 2 + 3, and 24 can only be 7 + 8 + 9.
2. So the middle row must hold 4, 5 and 6.
3. The column sums 12, 15, 18 then force the rows 1, 2, 3 / 4, 5, 6 / 7, 8, 9, so the centre cell is 5.

Teacher's Note:
1. The smallest and largest sums have only one way each.
2. Check the columns: 1 + 4 + 7 = 12, 2 + 5 + 8 = 15, 3 + 6 + 9 = 18.

Answer: (a) 13, odd

Explanation:
1. Each entry is the sum of the two before it.
2. So the number of 6-beat rhythms is 5 + 8 = 13.
3. 13 cannot be arranged fully in pairs, so it is odd.

Teacher's Note:
1. Use the Virahāṅka rule, not listing.
2. 13 = 6 pairs + 1 left over.