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If a and b are integers and ab ≠ 0, what is the units digit of ab? 21 Apr 2016, 00:44
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72% (00:51) correct 28% (00:39) wrong based on 75 sessions

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If a and b are integers and ab ≠ 0, what is the units digit of ab?

(1) a = 4!
(2) b = 7!
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B
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If a and b are integers and ab ≠ 0, what is the units digit of ab? 21 Apr 2016, 01:09
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Answer is B.
With just A, we know that the product of the two numbers will be a 4! = 24 X b. Can't make a comment on the unit's place digit with just this information.
With B, we know that the product of the two numbers will be a X 7! = a X 5040. In this case, the unit's digit will always be 0.
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If a and b are integers and ab ≠ 0, what is the units digit of ab? 21 Apr 2016, 10:21
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Aha!!

Was your adrenaline rushing like mine after seeing both the statements together? Cool. You may work that in your favour if you want. Keep your eyes open for such questions. THEY ARE TRAP C TYPES!!

S1:
4! = 24. Unit digit for the required product (ab) depends on unit digits of individual numbers. We know unit digit of one no but not other. Insufficient.

S2:
7! = Don't bother calculating. We know this no will have 5 and 2 among it's factors. This no should definitely end with 0. Furthermore, if you multiply another number to this, the product will again end up with 0 as its unit digit.
Sufficient.

Answer B.

Cheers!

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If a and b are integers and ab ≠ 0, what is the units digit of ab? 21 Apr 2016, 15:21
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Statement A gives 4! = 24

So, we get only the units digit of a
Not sufficient

Statement B gives 7 ! = 5040

Since the units digit of b is 0, the product of any number with 0 will give us 0

Statement B is sufficient

Correct Option : B
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If a and b are integers and ab ≠ 0, what is the units digit of ab? 22 Apr 2016, 00:57
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If a and b are integers and ab ≠ 0, what is the units digit of ab?

(1) a = 4!
(2) b = 7!

Note here are we are suppose to find unit digit for a factorial case . Hence we must look for 2,5 pair ... to get a sure shot answer .

1)only a is given and no idea about b --hence not sufficient
2) b = 7! . It is sufficient
why ?
7! = 1* 2*3*4*5*6*7*8
note we have combination of 2 and 5 .hence no matter what ever is a or even if a is not given . we know that unit digit is 0

Hence B ans .
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If a and b are integers and ab ≠ 0, what is the units digit of ab? 25 Apr 2016, 06:28
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are integers and ab ≠ 0, what is the units digit of ab?

(1) a = 4!
(2) b = 7!

In the original condition, there are 2 variables, which should match with the number of equations. So you need 2 equations.
For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), from ab=(4!)(7!)=........0, 0 for ones is derived, which is unique and sufficient.
So, the answer is C. However, this is an integer question, which is one of the key questions.
Apply the mistake type 4(A). For 1), if b=5, 0 is derived.
If b=1, 4 is derived, which is not unique and not sufficient.
For 2), b=7!=.........0 is derived(as it includes 2 and 5) and ab=..........0 is derived, which is unique and sufficient.
Thus, when both C and B are likely to be an answer, the answer is B.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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