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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 27 May 2019, 21:10
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E
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55% (hard)

Question Stats:

63% (01:54) correct 37% (02:09) wrong based on 313 sessions

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The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96
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E
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 27 May 2019, 21:24
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nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96
Show more
let the numbers be 24x and 24y where x and y are co-prime.

24(x+y) = 144, x+y= 6
Possible values of x and y
1, 5: for co prime.

So Difference is 96 E
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 30 May 2019, 13:31
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What does HCF stand for? I got this term in another question but still I have no idea what it is and what I should know about it.
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 30 May 2019, 13:40
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HCF => Highest common factor of two numbers
For example- Take two numbers 4 and 6
4=1*2*2 and 6=1*2*3
HCF(4,6)=2*1=2

Take another example
HCF(4,9)=1
4=1*2*2 and 9=1*3*3


DarleneTran
What does HCF stand for? I got this term in another question but still I have no idea what it is and what I should know about it.
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 30 May 2019, 15:56
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What does HCF stand for? I got this term in another question but still I have no idea what it is and what I should know about it.
Show more

Check this post by ArvindCrackVerbal

HCF & LCM
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 20 Jul 2020, 01:33
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nick1816 Requesting you to please post an alternate approach. I tried this approach with a different set of values but didnt work .



LeoN88
nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96
let the numbers be 24x and 24y where x and y are co-prime.

24(x+y) = 144, x+y= 6
Possible values of x and y
1, 5: for co prime.

So Difference is 96 E
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 20 Jul 2020, 01:42
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VERBAL1
nick1816 Requesting you to please post an alternate approach. I tried this approach with a different set of values but didnt work .



LeoN88
nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96
let the numbers be 24x and 24y where x and y are co-prime.

24(x+y) = 144, x+y= 6
Possible values of x and y
1, 5: for co prime.

So Difference is 96 E
Show more

there is no alternative solution.

the numbers are 24k and 24m where k and m are co-primes. so, 24(k+m)=144. That makes (k+m)=6. There are 7 cases (i.e. k=0,m=6 or k=1,m=5 or k=2,m=4 or k=3,m=3 or k=4,m=2 or k=5,m=1 or k=6,m=0) the only case in which k and m are co-prime is k=1, m=5 (or vice versa but it will not change the difference)
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 29 Jul 2020, 06:37
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nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96
Show more


nick1816, C can also be the answer here. Here is my what I did

Given
a + b = 144; GCD = 24, which means both the numbers a & b have a 24 in common. Therefore, I can write a & b as --> a + b = 24 (6).

The remaining factors of a & b add up to 6. These factors can be written for a & b as --> a = 1, b = 5; a = 2, b = 4; a = 5, b = 1; a = 4, b = 2; a= 3, b = 3 not possible since that does not work with the given GCD then

So with all those combinations above you end up with the following values for a & b by multiplying the GCD with the above combinations

--> a = 1(24), b = 5(24) --> a = 24, b = 120 [a + b = 144]
--> a = 2(24), b = 4(24) --> a = 48, b = 96 [a + b = 144]
--> a = 120, b = 24 [Interchanged]
--> a = 96, b = 48 [Interchanged]

From the solutions above, you can have both 48 and 96 as the solutions here. Are the answer choices accurate ? If I've done something wrong, please guide me.

Thanks
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 29 Jul 2020, 06:56
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SiddharthR
nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96


nick1816, C can also be the answer here. Here is my what I did

Given
a + b = 144; GCD = 24, which means both the numbers a & b have a 24 in common. Therefore, I can write a & b as --> a + b = 24 (6).

The remaining factors of a & b add up to 6. These factors can be written for a & b as --> a = 1, b = 5; a = 2, b = 4; a = 5, b = 1; a = 4, b = 2; a= 3, b = 3 not possible since that does not work with the given GCD then

So with all those combinations above you end up with the following values for a & b by multiplying the GCD with the above combinations

--> a = 1(24), b = 5(24) --> a = 24, b = 120 [a + b = 144]
--> a = 2(24), b = 4(24) --> a = 48, b = 96 [a + b = 144]
--> a = 120, b = 24 [Interchanged]
--> a = 96, b = 48 [Interchanged]

From the solutions above, you can have both 48 and 96 as the solutions here. Are the answer choices accurate ? If I've done something wrong, please guide me.

Thanks
Show more

HCF of 48 and 96 is 48, not 24.

Posted from my mobile device
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 29 Jul 2020, 07:40
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tyildirim92
SiddharthR
nick1816
The sum of 2 numbers is 144 and their HCF is 24. Find the difference between the numbers?

A. 0
B. 24
C. 48
D. 72
E. 96


nick1816, C can also be the answer here. Here is my what I did

Given
a + b = 144; GCD = 24, which means both the numbers a & b have a 24 in common. Therefore, I can write a & b as --> a + b = 24 (6).

The remaining factors of a & b add up to 6. These factors can be written for a & b as --> a = 1, b = 5; a = 2, b = 4; a = 5, b = 1; a = 4, b = 2; a= 3, b = 3 not possible since that does not work with the given GCD then

So with all those combinations above you end up with the following values for a & b by multiplying the GCD with the above combinations

--> a = 1(24), b = 5(24) --> a = 24, b = 120 [a + b = 144]
--> a = 2(24), b = 4(24) --> a = 48, b = 96 [a + b = 144]
--> a = 120, b = 24 [Interchanged]
--> a = 96, b = 48 [Interchanged]

From the solutions above, you can have both 48 and 96 as the solutions here. Are the answer choices accurate ? If I've done something wrong, please guide me.

Thanks

HCF of 48 and 96 is 48, not 24.

Posted from my mobile device
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Perfect. caught the error. Thanks bud !
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 29 Jul 2020, 09:17
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x+y=144
GCF = 24

(x+24)+(y+24)=144
x+y=144-48
x+y=96
x-y=-96

E
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 21 Aug 2020, 00:01
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a + b = 144

Since the Greatest Common Factor between the 2 Numbers = 24, the 2 Numbers can NOT share any more Prime Factors. Further, both are Multiples of 24.


a = 24 * (x)

b = 24 * (y)

x and y must be CO-PRIME, in that they do NOT share any Prime Factors. Otherwise, the G.C.F. would not be 24. It would be 24 * whatever other Prime Factors the 2 numbers shared.

Substituting into a + b = 144

24 * x + 24 * y = 144

x + y = 6

x and y can not = 3 and 3, because then the G.C.F. would = 24 * 3

x and y can not = 2 and 4, because then the 2 numbers would share another 2 Prime Factor and the G.C.F. would = 24 * 2

x must be 1 and y must be 5, or vice-versa.

24 * 1 = 24
24 * 5 = 120

and finally, 120 - 24 = 96. Answer Choice E
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The sum of 2 numbers is 144 and their HCF is 24. Find the difference b 03 Jun 2025, 04:16
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