MATHS 5 Marks Questions

(a) (-348) + (-1064)
Add two negative numbers → keep negative, add absolute values:
-348 + (-1064) = -1412.
(b) (-348) – (-1064)
Subtracting a negative → same as adding positive:
-348 – (-1064) = -348 + 1064 = 716.
(c) 348 – (-1064)
Subtracting a negative → add positive.
348 – (-1064) = 348 + 1064 = 1412.
(d) (-348) × (-1064)
Negative × Negative = Positive
(-348) × (-1064) = 370272
(e) 348 × (-1064)
Positive × Negative = Negative
348 × (-1064) = -370272
(f) 348 × 964
Positive × Positive = Positive
348 × 964 = 335472
Arranging in increasing order:
(e) 370272, (a) -1412, (b) 716, (c) 1412, (f) 335472, (d) 370272
Hence, (e) < (a) < (b) < (c) < (f) < (d).

(a) Let three consecutive numbers be n – 1, n, and n + 1.
Then product = (n – 1) (n) (n + 1) = -6
The only consecutive integers whose product is -6 are -2, -1, and 0.
But -2 × -1 × o = 0, not possible.
Consecutive numbers are integers.
The product is negative, so there must be an odd number of negative integers.
Integers are -2, -1, 1.
Their product = – 2 × -1 × 1 = 2, not possible
Integers are -3, -2, -1.
Their product = [-3 × -2] × -1 = 6 × -1 = -6
Hence, consecutive integers are -3, -2, -1.
(b) Let three consecutive numbers be n – 1, n, and n + 1.
∴ (n – 1) (n) (n + 1) = 120
Now the cube root of 120 = 4.93
So n is likely to be 5.
∴ (5 – 1) × (5) × (5 + 1) = 4 × 5 × 6 = 120
Hence, consecutive integers are 4, 5, and 6.

(a) Here, 4 × (-3) = – [(4) × (3)] = -12
(∵ Multiplier is positive and the multiplicand is negative, their product is negative)
(b) Here, (-6) × (-3) = 6 × 3 = 18
(∵ Both the multiplier and multiplicand are negative; their product is positive)
(c) Here, (-5) × (-1) = 5 × 1 = 5
(∵ Both the multiplier and multiplicand are negative; their product is positive)
(d) Here, (-8) × 4 = -(8 × 4) = -32
(∵ Multiplier is negative and multiplicand is positive, their product is negative)
(e) Here, (-9) × 10 = -(9 × 10) = -90
(∵ Multiplier is negative and multiplicand is positive, their product is negative)
(f) Here, 10 × (-17) = -(10 × 17) = -170
(∵ Multiplier is positive and multiplicand is negative, their product is negative)

(a) Profit on one white cement bag = ₹ 8
Loss on one grey cement bag = ₹ 5
Profit from selling white cement = 3000 bags × ₹ 8/bag = ₹ 24000
Loss from selling white cement = 5000 bags × ₹ 5/bag = ₹ 25,000
[∵ loss is more than profit, i.e., loss]
Total loss = 25,000 – 24,000 = 1,000
∴ The company has a loss of ₹ 1000.
(b) Let x be the number of white cement bags sold.
Total profit/loss is zero.
Profit from white cement + Loss from grey cement = 0
⇒ x × 8 + 6400 × (-5) = 0
⇒ 8x – 32000 = 0
⇒ x = 4000
∴ The company must sell 4000 bags of white cement to make neither profit nor loss.

(a) Sum = 27, Difference = 9

First number	Second number	Sum	Difference
20	7	27	13
17	10	27	7
16	11	27	5
18	9	27	9

Hence correct pair is (18, 9).
(b) Sum = 4, Difference = 12

First number	Second number	Sum	Difference
2	2	4	0
4	0	4	4
10	-6	4	16
8	-4	4	12

Hence correct pair is (8, -4).
(c) Sum = 0, Difference = 10

First number	Second number	Sum	Difference
6	-6	0	12
8	-8	0	16
7	-7	0	14
5	-5	0	10

Hence correct pair is (5, -5).
(d) Sum = 0, Difference = -10

First number	Second number	Sum	Difference
4	-4	0	8
3	-3	0	6
-5	5	0	-10
8	-8	0	16

Hence correct pair is (8, -8).
(e) Sum = -7, Difference = -1

First number	Second number	Sum	Difference
-9	2	-7	-11
1	-8	-7	9
-6	-1	-7	-5
-4	-3	-7	-1

Hence, the correct pair is (-4, -3).
(f) Sum = -7, Difference = -13

First number	Second number	Sum	Difference
-4	-3	-7	-1
-8	1	-7	-9
-3	-4	-7	+5
-10	3	-7	-13

Hence correct pair is (-10, 3).