| Exercise-I |
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| 1. c |
2. b |
3. c |
4. d |
5. b |
| 6. c |
7. b |
8. b |
9. c |
10. c |
| 11. c |
12. b |
13. a |
| 1. |
The sum of two numbers is 100 and their difference is 37. The largest number is |
| Sol: |
Let numbers be x, 100 – x |
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x – (100 – x) |
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37 |
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x – 100 + x |
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37 |
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2x |
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137 |
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x |
= |
68.5 |
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The two numbers are 68.5 and 100 – 68.5 i.e., 68.5 and 31.5 |
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Largest number |
= |
68.5 |
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| 2. |
The difference of two numbers is 5 and the difference of their squares is 135. The sum of the numbers is |
| Sol: |
Let numbers be x and y |
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x – y = 5, x2 – y2 = 135 |
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(x + y)(x – y) |
= |
135 |
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put x – y |
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5 |
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(x + y) × 5 |
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135 |
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x + y |
= |
 |
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x + y |
= |
27 |
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| 3. |
The difference of two numbers is 8 and  of their sum is 35. The numbers are |
| Sol: |
Take the option (c) i.e., 136, 144 |
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144 – 136 |
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8 |
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 |
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The numbers 144, 136 satisfy the given conditions.
The numbers are 144 and 136. |
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| 4. |
Three fourth of four fifth of a number is 120. The number is |
| Sol: |
Let the number be x |
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 |
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120 |
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x |
= |
 |
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x |
= |
200 |
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| 5. |
24 is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. The 2nd part is |
| Sol: |
Let 1st part be x and 2nd part be (24 – x) |
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7(x) + 5(24 – x) |
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146 |
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7x + 120 – 5x |
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146 |
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2x |
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26 |
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x |
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13 |
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The 2nd part is 24 – x i.e., 24 – 13 = 11 |
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| 6. |
A positive number when decreased by 4, is equal to 21 times the reciprocal of the number. The number is |
| Sol: |
Let number be x |
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x – 4 |
= |
 |
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put x |
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7 |
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7 – 4 |
= |
 |
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3 |
= |
3 |
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 x |
= |
7 is the number |
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| 7. |
The sum of two numbers is twice their difference. If one of the number is 10, the other number is |
| Sol: |
Let the numbers be x and y |
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x + y |
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2(x – y) |
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x + y |
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2x – 2y |
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x |
= |
3y |
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If y = 10 then x = 3 × 10 |
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x |
= |
30 |
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Number is 30 |
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| 8. |
The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is |
| Sol: |
Let numbers be x and y |
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xy = 120, x2 + y2 = 289 |
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(x + y)2 |
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x2 + y2 + 2xy |
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= |
289 + 2 × 120 |
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= |
289 + 240 |
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(x + y)2 |
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529 |
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x + y |
= |
 |
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x + y |
= |
23 |
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| 9. |
A number whose fifth part increased by 5 is equal to its 4th part diminished by 5 is |
| Sol: |
Let the number be x |
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 |
= |
 |
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5 + 5 |
= |
 |
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10 |
= |
 |
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 |
= |
10 |
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x |
= |
10 × 20 = 200 |
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| 10. |
A certain number of two digits is 3 times the sum of its digits and if 45 is added to it, the digits are reversed. The number is |
| Sol: |
Consider number 27 |
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2 + 7 |
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9 [sum of digits] |
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sum of digits × 3 |
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27 |
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If 45 is added to 27 we get 72 |
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45 + 27 |
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72 [digits are reversed] |
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The number is 27 |
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| 11. |
Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of third and 52. The smallest number is |
| Sol: |
Let numbers be 3x, 4x, 5x |
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3x + 5x |
= |
52 + 4x |
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8x |
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52 + 4x |
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4x |
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52 |
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x |
= |
13 |
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Numbers are 3 × 13 = 39, 4 × 13 = 52, 5 × 13 = 65 |
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Smallest number is 39 |
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| 12. |
If  then x = |
| Sol: |
12(3 + x) |
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11(4 + x) |
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36 + 12x |
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44 + 11x |
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12x – 11x |
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44 – 36 |
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x |
= |
8 |
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| 13. |
Of the three numbers, the first is twice the second and is half of the third. If the average of three numbers is 56, the smallest number is |
| Sol: |
Let 3 numbers be a, b, c |
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a = 2b, a =  c |
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a = 2b, c = 2a → c = 2 × 2b = 4b |
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 |
= |
56 |
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 |
= |
56 |
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7b |
= |
56 × 3 |
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b |
= |
 |
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b |
= |
24 |
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SAT Math 
