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The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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25 Apr 2016, 08:12
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41% (01:41) correct 59% (01:24) wrong based on 128 sessions
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Re: The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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25 Apr 2016, 09:04
Bunuel wrote: The product of the units digit, the tens digit, the hundreds digit, and the thousands digit of the positive integer k is 54. What is the tens digit of k?
(1) k is even
(2) The tens digit of k is 1 larger than the units digit of k so we look at the ways we can factor 54 in four single digit factors.. 54 = 1*1*6*9.. 54 = 1*2*3*9.. 54 = 2*3*3*3lets see the statements (1) k is evenso number can be .. 1196 1916 1932 1392 different tens digit Insuff (2) The tens digit of k is 1 larger than the units digit of kthe number can be 9321 9132.. again different tens digit Insuff combined..the last digit has to be 2 and the tens digit is ONE more than the units digit.. so tens digit = 2+1 = 3 suff C
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Re: The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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05 Nov 2016, 10:38
The product of the units digit, the tens digit, the hundreds digit, and the thousands digit of the positive integer k is 54. What is the tens digit of k?
(1) k is even
(2) The tens digit of k is 1 larger than the units digit of k
> Step 1 : Extract the information from question stem : 54 can be represented as :  __ 1 * 54 = 1 * 9 * 6 = 1 * 3 * 3 * 6 or 1 * 9 * 3 * 2  __ 2 * 27 = 2 * 9 * 3 = 2 * 3 * 3 * 3  __ 3 * 18 = 3 * 9 * 2 = 3 * 3 * 3 * 2 = 3 * 6 * 3 = 3 * 3 * 2 * 3 Different possibilities are 1336 1932 2333
Prime Factors of 54 are 3 & 2 Step 2 : State the goal : We need to find the tens digit of K ?
Step 3 : Satisfy the fact condition and try to disprove or to find the results for question stem
1. K is even so units digit must be any of 2, 4, 6, 8 : 54 is not divisible by 4 & 8 so no combination will yield 4 or 8 so exclude if tens digit is 2 then k can be 1932 if tens digit is 6 then k can be 1336 Two different solution satisfying the fact. Not sufficient
2. Tens digit is 1 larger than the units digit From different possibilities we can see 1932 or 9321 can yield two different possibilities. Not sufficient Both 1 & 2 : K is even and tens digit 1 larger than units digit : 1932 is the only combination which satisfies the both the fact and yields the answer for question.
Step 4 : Answer choice C is correct AD BCE



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Re: The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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28 Nov 2016, 02:22
let the number be  abcd a*b*c*d = 54 1) d is even i.e d can be 2 4 6 8 but 4 and 8 are not factors of 54 so we are left with 2 and 6 .. still we can not say anything about c. insufficient 2)c = d+1 d can be 1,2,3,9,6 so if d is 1 c can be 2 but if d is 2 c can be 3 Insufficient 1)+2) we know d is either 2 or 6 so c can be 7 or 3 but 7 is not a factor of 54 so we definitely know that c is 3 Sufficient



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Re: The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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01 Jan 2018, 11:42
Bunuel wrote: The product of the units digit, the tens digit, the hundreds digit, and the thousands digit of the positive integer k is 54. What is the tens digit of k?
(1) k is even
(2) The tens digit of k is 1 larger than the units digit of k VERITAS PREP OFFICIAL SOLUTION:You need four digits that multiply to 54, so begin by factoring 54 with a factor tree: 54 = 2 x 3 x 3 x 3 Since 54 is composed of the prime factors 2, 3, 3, and 3, you might be tempted to conclude that the four digits of the integer must themselves be 2, 3, 3, and 3. For example: 3 3 2 3 or 3 3 3 2 However, other options exist. If you multiply 2 by 3 we could have 6 as one of the digits and the remaining digit could be 1: 6 3 3 1 Or, you could multiply 3 by 3 giving 9 as one of the digits: 3 9 1 2 Statement 1: Since k is even, the units digit of k must be even. The units digit of k could be 2 or 6, giving possibilities such as the following: 3 3 3 2 3 3 1 6 1 1 9 6 The tens digit could then be 1, 3, or 9, so Statement 1 is insufficient. Statement 2: Search for digit pairs that are one unit apart. 2 and 3 are one such pair, as is 1 and 2. Examples include: 3 3 3 2 > tens digit is 1 larger than units digit 3 9 2 1 > tens digit is 1 larger than units digit The tens digit could either be 2 or 3. INSUFFICIENT Together: Combining the two statements, you should see that 1932 and 3332 are the only possibilities, thus the correct answer is C.
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Re: The product of the units digit, the tens digit, the hundreds digit, an [#permalink]
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09 Jan 2018, 05:20
Bunuel wrote: The product of the units digit, the tens digit, the hundreds digit, and the thousands digit of the positive integer k is 54. What is the tens digit of k?
(1) k is even
(2) The tens digit of k is 1 larger than the units digit of k 54 = 3^3 * 2 {1, 2, 3, 9}, {1, 1, 6, 9} Statement 1: Number = 3912 or 9132 i.e. different tens digit NOT SUFFICIENT Statement 2: Number = 3921 or 9132 i.e. different tens digit NOT SUFFICIENT Combining The two statements Number = xx32 Sufficient Answer: Option C
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