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Retired Moderator V
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What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 56% (01:35) correct 44% (01:39) wrong based on 38 sessions

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GMATbuster's Weekly Quant Quiz#8 Ques #8

What Is the units digit of positive Integer x?
1) 7, 15, 24, and n are all factors of x.
2) 6! < x < 7!

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NUS School Moderator V
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Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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From statement 1:

7,15,24 and n are factors of x.
Then LCM of 7,15,24 and n will contain unit digit Zero. Since 15*24 will give a unit digit zero.
Hence Sufficient.

From statement 2:

6!<x<7!
6! = 720 and 7! = 5040
X can be 721 or 722 or any other integer.
Hence unit digit is not the same
Insufficient.

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GMAT 1: 610 Q48 V25 GMAT 2: 690 Q50 V32 GMAT 3: 710 Q50 V36 Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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1
What Is the units digit of positive Integer x?
1) 7, 15, 24, and n are all factors of x.
2) 6! < x < 7!

COncept: if a number is divisible by 2 and 5 then last digit is 0.

So stat 1:

If 15 and 24 are factors
it means 15 and 24 divide x
hence 5 and 2 are also factors of x
THus last digit(unit digit) is 0.

A sufficient

Stat 2:
6!=720
7!=5040

X could be any value so the number has a large range.
Hence Not sufficient.

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Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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Stmt 1: x will have prime factors 2,3,5,7 for sure and may have some more. But since 2*5 = 10, anything multiplied after that, will always have 0 in units digit. Hence sufficient.

Stmt 2: 6! = 720, 7! = 5040, there are many integers between these two numbers, hence insufficient.

Hence Option A
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Intern  B
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Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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OPTION A
1) LCM OF THE NUMBERS WILL END IN 0. SO SUFFICIENT
2) VALUE CAN BE ANYWHERE BETWEEN 720 AND 5040. INSUFFICIENT
Intern  B
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Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a  [#permalink]

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st1::

lcm 7,15,24,n= 840n

the number is 840n, hence the unit digit should be 0
hence st1 is sufficient

st2:

720 <x<5040
x can take any value in this range
hence the st is insufficient

Ans : A Re: What Is the units digit of positive Integer x? 1) 7, 15, 24, and n a   [#permalink] 10 Nov 2018, 11:22
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