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Which is greater 35,043*25,430 or 35,430*25,043?
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Updated on: 28 Feb 2019, 01:17
Updated on: 28 Feb 2019, 01:17
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Question Stats:
40% (00:54) correct
59% (00:49) wrong based on 104 sessions
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Quantity A |
Quantity B |
\(35,043*25,430\) |
\(35,430*25,043\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Diagnostic #3
Re: Which is greater 35,043*25,430 or 35,430*25,043?
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28 Feb 2019, 14:15
28 Feb 2019, 14:15
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There's also a handy trick here using a special property. The sum of the two numbers in each quantity is the same. When this is the case, the maximum product will be when both numbers are equal. The farther the numbers get from equality, the lower their product will be.
This is easiest to understand with an example. Say the sum of two numbers is 10. Their product will be the biggest if each one is 5. So 5*5 > 6*4. And the product will get less and less as the numbers diverge. So:
5*5 > 6*4 > 7*3 > 8*2 > 9*1 > 10*0
So if the sum of two numbers stays the same, their product will be bigger when they're closer together, and smaller when they're farther apart.
Since the sum of both quantities is the same, we can just look to see which numbers are closer together (that is, which have a smaller difference). 35,043 and 25,430 are closer together than 35,430 and 25,043 are. Hence, 35,043*25,430 > 35,430*25,043.
This is easiest to understand with an example. Say the sum of two numbers is 10. Their product will be the biggest if each one is 5. So 5*5 > 6*4. And the product will get less and less as the numbers diverge. So:
5*5 > 6*4 > 7*3 > 8*2 > 9*1 > 10*0
So if the sum of two numbers stays the same, their product will be bigger when they're closer together, and smaller when they're farther apart.
Since the sum of both quantities is the same, we can just look to see which numbers are closer together (that is, which have a smaller difference). 35,043 and 25,430 are closer together than 35,430 and 25,043 are. Hence, 35,043*25,430 > 35,430*25,043.
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Which is greater 35,043*25,430 or 35,430*25,043?
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24 Feb 2019, 06:17
24 Feb 2019, 06:17
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chetan2u wrote:
Quantity A |
Quantity B |
\(35,043*25,430\) |
\(35,430*25,043\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Diagnostic #3
We can solve this question using matching operations
Given:
Quantity A: (35,043)(25,430)
Quantity B: (35,430)(25,043)
Divide both quantities by 35,043 to get:
Quantity A: (25,430)
Quantity B: (35,430)(25,043)/(35,043)
Divide both quantities by 25,043 to get:
Quantity A: (25,430)/(25,043)
Quantity B: (35,430)/(35,043)
Rewrite the numerators to get:
Quantity A: (25,043 + 387)/(25,043)
Quantity B: (35,043 + 387)/(35,043)
USEFUL PROPERTY: (a + b)/c = a/c + b/c
Apply above property to get:
Quantity A: 25,043/25,043 + 387/25,043
Quantity B: 35,043/35,043 + 387/35,043
Simplify to get:
Quantity A: 1 + 387/25,043
Quantity B: 1 + 387/35,043
Subtract 1 from both quantities to get:
Quantity A: 387/25,043
Quantity B: 387/35,043
Since 35,043 > 25,043, we know that 387/35,043 < 387/25,043
Answer: A
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