Directions (1-5): In the following questions three equations numbered I, II and III are given. You have to solve all the equations either together or separately, or two together and one separately, or by any other method and
Give answer If
(a) x < y = z
(b) x < y < z
(c) x < y > z
(d) x = y > z
(e) x = y = z or if none of the above relationship is established
Q1. I. 7x + 6y + 4z = 122
II. 4x + 5y + 3z = 88
III.9x + 2y + z = 78
Q2. I. 7x + 6y = 110
II. 4x + 3y = 59
III. x + z = 15
Q3. I.
II. 2y + 3z = 33
III.6y + 5z = 71
Q4. I. 8x + 7y = 135
II. 5x + 6y = 99
III. 9y + 8z = 121
Q5. I. (x + y)3 = 1331
II. x - y + z = 0
III. xy = 28
Directions (6-10): Study the following pie-charts carefully and answer the questions given below.
Total population of the world = 700 crore
Number of patients = 10% of the total population
Percentage of all the patients in various continents
Percentage of patients of various diseases in the world
Percentage of cancer patients in various continents
Q6. The number of cancer patients in Australia is what per cent of the total number of patients of heart disease in the world?
(a) 6.81%
(b) 7.85%
(c) 5.49%
(d) 6.01%
(e) 7.98%
Q7. If the number of cancer patients in South America decreases by 25%, what is the percentage decrease in total number of cancer patients in the world?
(a) 4%
(b) 8%
(c) 3%
(d) 6%
(e) 5%
Q8. What is the ratio of the total number of patients in Africa to the total number of cancer patients in Asia and North America together?
(a) 350 : 147
(b) 360 : 347
(c) 350 : 334
(d) 352 : 250
(e) None of these
Q9. If the total number of patients increases by 10% every year in Europe then what is the difference between the total number of patients in Europe after 2 years and the total number of cancer patients in South America now?
(a) 8 lakh
(b) 9 lakh
(c) 6 lakh
(d) 7 lakh
(e) 5 lakh
Q10. If the number of hepatitis patients increases by 6% and that of heart disease ones by 22%, what will be their new ratio?
(a) 1110 : 2396
(b) 1245 : 4925
(c) 1113 : 4697
(d) 1346 : 3411
(e) 1496 : 2541
Directions (11-15): What approximate value will come in place of the question mark (?) in the given questions? (You are not expected to calculate the exact value)
(a) 1315
(b) 1365
(c) 1215
(d) 1465
(e) 1265
(a) 285
(b) 225
(c) 345
(d) 150
(e) 185
Q13. 899.99 ÷ 45.012 = ? - 224.488
(a) 185
(b) 395
(c) 295
(d) 245
(e) 355
(a) 77586
(b) 77776
(c) 79566
(d) 78356
(e) 76876
(a) 32
(b) 16
(c) 64
(d) 256
(e) 512
Solutions
S1. Ans.(a)
Sol. 7x + 6y + 4z = 122 ... (i)
4x + 5y + 3z = 88 ... (ii)
9x + 2y + z = 78 ... (iii)
By equation (iii) × 3 - equation (ii),
23x + y = 146 ...(iv)
By equation (iii) × 4 - equation (i),
29x + 2y = 190 ...(v)
By equation (iv) × 2 - equation (v)
17x = 102
x = 6
From equation (iv),
23 × 6 + y = 146
y = 146 - 138 = 8
From equation (iii),
9 × 6 + 2 × 8 + z = 78
54 + 16 + z = 78
z = 78 - 70 = 8
Clearly, x < y = z
S2. Ans.(c)
Sol. By equation II × 2 - equation (I)
x = 8
From equation (I),
7 × 8 + 6y = 110
6y = 110 - 56 = 54
y = 9
From equation (III),
8 + z =15
z = 7
Clearly, x < y > z
S3. Ans.(e)
By equation II × 3 - equation I
4z = 28
z = 7
From equation II,
2y + 3 × 7 = 33
2y = 33 - 21 = 12
y = 6
x = y < z
S4. Ans.(d)
Sol. By equation I × 5 - II × 8
y = 9
From equation I,
8x + 7 × 9 = 135
8x = 135 - 63 = 72
x = 9
From equation III,
9 × 9 + 8z = 121
8z = 121 - 81 = 40
z = 5
Clearly, x = y > z
S5. Ans.(e)
Sol. (x + y)3 = 1331
ð x + y = 11
ð y = 11 - x
From equation III,
x (11 - x) = 28
ð 11x - x2 = 28
x2 - 11x + 28 = 0
x2 - 7x - 4x + 28 = 0
x (x - 7) - 4 (x - 7) = 0
(x - 7) (x - 4) = 0
x = 7, 4
From equation I
y = 4, 7
From equation II
7 - 4 + z = 0 => z = -3
or, 4 - 7 + z = 0 => z = 3
S6. Ans.(a)
Sol.
S7. Ans.(c)
Sol.
S8. Ans.(a)
Sol.
S9. Ans.(d)
Sol.
S10. Ans.(c)
Sol.
S12. Ans.(c)
Sol. 399.15-12×13.95+ ?=(24.02)^2
Or 400 - 12 × 14 + ? ≈ 576
Or 400 - 168 + ? ≈ 576
Or ? ≈ 576 - 400 + 168
Or ? ≈ 344 ≈ 345
S13. Ans.(d)
Sol. Here, the given expression can be written as
900 ÷ 45 = ? - 225
Or 20 = ? - 225
Or ? = 225 + 20
Or ? = 245
S14. Ans.(c)
Sol. Here, the given expression can be rounded off as
13×7+(85)^2×11= ?
Or 91 + 7225 × 11 = ?
Or 91 + 79475 = ?
Or ? ≈ 79566
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