Pat took N whole Days
That means N(x)
1 Day= 24 hours

so x=24
24(N)--> Whatever the answers is , it should be multiple of 24.
As per cyclicity method --> 4 has cyclicity (4&6)

So 6_36 is answer (as its ends with 6)

What is this question trying to ask? Could you please throw some light on it? It is ambiguous

Question seems incomplete to me. I think 4 digit number with missing digit should represent total # of hours spent on the project. At least in this case it has some sense.

1 day = 24 hours = 8*3. Number should be divisible by 8 (and 4 as a result). Only option that fits is b.

May be somebody has better insight.

My apologies. The question has been edited.

My apologies. The question has been edited.

The answer given by you is correct.

Total number of hours = N*24

So the total number of hours has to be a multiple of 24. To find out if the number of hours is divisible by 24, we need to know all the digits. However the question stem says which of the values could be the number of hours so we need to eliminate answer choices based on the information we have.

We know that the number is divisible by 24, hence the number should be divisible by 4.

To find if the number is divisible by 4, we only need to check if the number formed by the last 2 digits is divisible by 4. We do not need the missing digit to know if the number is divisible by 4. All the options have the last 2 digits so we can check the divisibility by 4.
a) number formed by last 2 digits = 98 . Not divisible by 4
b) number formed by last 2 digits = 36 . Divisible by 4
c) number formed by last 2 digits = 50 . Not divisible by 4
d) number formed by last 2 digits = 90 . Not divisible by 4
e) number formed by last 2 digits = 62 . Not divisible by 4

Hence we can see that whatever the missing digit may be, options a,c,d and e will never be divisible by 4 and hence also not divisible by 24.

Answer is B.

I brute forced it.

24X100=2400

2400
4800
7200

7200-240 = 6960 - 24 = 6936

Since there are 24 hours in a day, the number needs to be divisible by 24. Any number divisible by 24 must also be divisible by 4. A number is divisible by 4 when the last two digits of that number are divisible by 4. Since 36/4 = integer, 6_36 is the correct answer.

Answer: B
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how do we know that any number divisible by 24 must also be divisible by 4 ? could you explain a bit more??

Well 4 is a factor of 24 right? In other words 24 is a MULTIPLE OF 4. Thus, any number that is a multiple of 24 (or divisible by 24) is also divisible by 4.

For instance, 24, 48, 72, 96.... are all divisible by 24 and also by 4 right?
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How did you limit it to 4 as against others factors such as 2,6 etc.. ?

Posted from my mobile device

Incorrect explanation. I do not agree. THe complete bnumber ahould be divisible by 8.

I don't think it has to do with divisibility rule. The number has to be divisible by 3 as well not just 8,
But if we see the question in the light of tens digit of 24 multiples.
24*N (any integer = n)
We will never find any number N which when multiplied with 24 leaves 98,90,50 or 62 as tens and ones digit combination

You can check by putting values in _ 6000 and 9000 is divisible by 24
We just have to check for 3 digit number which are divisible by 24. And there are only 37 such digits. Or you can use cyclicity of 4, which is the unit digit of 24 and has same multiplication and divisible concept as 24
We considered 4 because of same reason, not because it's a factor of 24

Posted from my mobile device

Given: Pat took 'N' whole days to complete the project.
Asked: If the dash represents the digit which has been omitted, then which of the following could be the number of hours that he took to complete the project?

Number of hours = Number of days * 24 = 24k ; where k is an integer

24*250 = 6000
24k = {24,48,72,96,120,144,168,192,240,264,288,312,336,...}
6336 is could be number of hours Pat took to complete the project.

IMO B
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Is that explanation really correct? ScottTargetTestPrep
I don't get why we should apply the cyclicity method.

For instance, 24*3 = 72 which is also a multiple by 24 and ends with a digit of 2, same applies to 24*17 = 408 ending in 8 and is still obviously a multiple of 24.
What the user above suggests, correct me if I am wrong, is seeking for a number which only consists of powers of 24 so -> 24^1, 24^2, 24^3 ... etc.
Is that really right?
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1 Day = 24 hours

If he completed N Whole Days, then N must be an Integer

Therefore, when we convert the N Days into Hours:

N Days * 24 hours / 1 Day = 24 * N

The Answer Choice must be a Multiple of 24


Rule 1: in order for an Answer Choice Number to be Divisible by 24, it must also be Divisible by the Factors of 24 - such as 4.

Rule 2: Divisibility Rule for any (2)^N Power ---- check whether the LAST N Digits of the Number are Divisible by (2)^N

4 = (2)^2 ----- Check whether the Last 2 Digits of Each Answer Choice is Divisible by 4

Using the Divisibility Rule for 4: only the LAST 2 Digits of Answer Choice B are Divisible by 4

Only -B- could represent a Whole Integer Number of N Days represented as Hours

Just attempted this question. I did it as follows:

24x1 = 24
24x2 = 48
24x3 = 72
24x4 = 96
24x5 = 120
24x6 = 144
24x7 = 168
24x8 = 192
24x9 = 216
24x10 = 240

So, you can NOT have:
1. Even number at tenth place, if unit digit is 0 - C and D eliminated
2. Even number at tenth place, if unit digit is 2 - E eliminated
3. Odd number at tenth place, if unit digit is 8 - A eliminated

But you can have,
Odd number at tenth place, if unit digit is 6 - B opted.

Saved a lot of time.

Hope it helps.
Cheers