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2ab5 is a four-digit number divisible by 25. If the number formed from

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2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 16:14
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2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

(A) 10
(B) 25
(C) 52
(D) 65
(E) 75

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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 17:47
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A number is divisible by 25 if the last 2 digits are divisible by 25. Only Option C satisfies this requirement.

Alternatively, we can quickly eliminate A,B and E since they are not multiples of 13. So now we have to figure out which of C or D would make the number divisible by 25. Looking at choice C, the number would be 2525, which is clearly div by 25.

Answer: C
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 19:09
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carcass wrote:
2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

(A) 10
(B) 25
(C) 52
(D) 65
(E) 75

Kudos for the right solution AND explanation



Divisibility by 25 is when last two digits are div by 25..
Two digits div by 25 are 00,25,50,75..
We already have 5 as units digit, so tens digit has to be 2 or 7

So look for a choice where b is 2 or 7..only C
So number becomes 2525...

C
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 21:25
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The correct ans C
We know to a number to be divisible by 25 last 2 digits should be 25 or 00
Only option C full fill the criteria
Also as per the Question ab is divisible by 13
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 21:52
teaserbae wrote:
The correct ans C
We know to a number to be divisible by 25 last 2 digits should be 25 or 00
Only option C full fill the criteria
Also as per the Question ab is divisible by 13


Hello teaserbae,

The last two digits can also be 75 or 50 for a number to be divisible by 25. So on having last digit as 5, tens place must be 2 or 7.

Best,
Gladi
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 22:08
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carcass wrote:
2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

(A) 10
(B) 25
(C) 52
(D) 65
(E) 75

Kudos for the right solution AND explanation


Two approach to solve this problem:
First:
If a number is divisible by 25 if the last 2 digits are divisible by 25. Only Option C .

Second:
Check for the multiple of 13 from the options, we can quickly eliminate A,B and E . C or D would make the number divisible by 25. Looking at choice C, the number would be 2525, which is clearly div by 25.
Option C
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 04 Apr 2018, 22:42
Gladiator59 wrote:
teaserbae wrote:
The correct ans C
We know to a number to be divisible by 25 last 2 digits should be 25 or 00
Only option C full fill the criteria
Also as per the Question ab is divisible by 13


Hello teaserbae,

The last two digits can also be 75 or 50 for a number to be divisible by 25. So on having last digit as 5, tens place must be 2 or 7.

Best,
Gladi


Yes true I forget to mention 50 and 75. Thanks for mentioning it .
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from  [#permalink]

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New post 10 Apr 2018, 11:12
carcass wrote:
2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

(A) 10
(B) 25
(C) 52
(D) 65
(E) 75


Looking at the answer choices, only 52 and 65 are multiples of 13 (so we can reject the other choices). If ab = 52, then 2ab5 = 2525. If ab = 65, then 2ab5 = 2655. Recall that only numbers that end in 00, 25, 50, or 75 are divisible by 25, so the 4-digit number must be 2525, which means that ab = 52.

Answer: C
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Re: 2ab5 is a four-digit number divisible by 25. If the number formed from   [#permalink] 10 Apr 2018, 11:12
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