Question
Two positive integers multiply to 5070, with their
highest common factor being 13 and their sum amounting to 143. What is the difference between these two integers?Solution
Let the two numbers be ‘13a’ and ‘13b’ ATQ; 13a × 13b = 5070 So, (a × b) = 30 ……………………. (1) Also, 13a + 13b = 143 So, a + b = 11 Or, a = (11 – b) …………………... (2) Putting value of ‘a’ in equation (1), we have (11 – b) × b = 30 Or, 11b – b2 = 30 Or, b2 – 11b + 30 = 0 Or, b2 – 6b – 5b + 30 = 0 Or, b(b – 6) – 5(b – 6) = 0 Or, (b – 6)(b – 5) = 0 So, b = 6 or b = 5 So, the two numbers are = 13 × 5 = 65 and 13 × 6 = 78 Required difference = 78 - 65 = 13Â
Statements: Some cubs are puppies.
No puppy is a calf.
All kittens are puppies.
Conclusions: I. At least some cubs are calves.
Statements: All bulb are light.
                        No light is a tubelight.
Conclusions: I. Some light a...
In the question below there are three statements followed by three conclusions I, II and III. You have to take the three given statements to be true e...
In the question below are given some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be ...
Statement : Only pant is T-shirt
Some pant is Shirt
No shirt is jacket.
Conclusion
I. All T-shirt being Shirt is a possib...
Statements:
All tomatoes are potato.
Some tomatoes are carrot.
Only a few carrots are garlic.
No garlic is brinjal...
Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with co...
Statement:
I) No water is air
II) Some air are land
III) All land are floor
IV) Some fire are water
Conclusion:
In the question below some statements are given followed by two conclusions I and II. You have to take the given statements to be true even if they see...
Statements:Â Â Â Â Â Â Some pen are pencil.
All pencil are book.
Conclusions:Â Â Â Â Â Â I. Some pen are book.
II. Some book are ...
Relevant for Exams:
