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805+ (Hard)|   Arithmetic|      
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CAMANISHPARMAR
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If x is a three-digit number in which the hundreds digit is 1 greater 05 Apr 2020, 06:45
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B
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Difficulty:

95% (hard)

Question Stats:

32% (02:33) correct 68% (02:27) wrong based on 116 sessions

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If x is a three-digit number in which the hundreds digit is 1 greater than the tens digit and 2 greater than the units digit, then what is the value of x ?

1) When x is multiplied by 3, the tens digit of the result is 2.

2) When x is multiplied by 4, the units digit of the result is 2.
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B
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If x is a three-digit number in which the hundreds digit is 1 greater 05 Apr 2020, 07:22
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CAMANISHPARMAR
If x is a three-digit number in which the hundreds digit is 1 greater than the tens digit and 2 greater than the units digit, then what is the value of x ?

1) When x is multiplied by 3, the tens digit of the result is 2.

2) When x is multiplied by 4, the units digit of the result is 2.
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So, H T U
(y+2) (y+1) y

y can be max 7 and min 0.

Statement#1

876 and 543 both gives T digit as 2 when multiplied by 3. Insufficient!

Statement#2

Only 543 gives unit digit 2 when multiplied by 4. Sufficient!

B
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If x is a three-digit number in which the hundreds digit is 1 greater 05 Apr 2020, 10:41
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CAMANISHPARMAR
If x is a three-digit number in which the hundreds digit is 1 greater than the tens digit and 2 greater than the units digit, then what is the value of x ?

1) When x is multiplied by 3, the tens digit of the result is 2.

2) When x is multiplied by 4, the units digit of the result is 2.
Show more

3 digit number x=abc
a=b+1
a=c+2
Statement 1: b=2, when abc is multiplied by 3
Lets make b=4, c=3,a=5
The number is 543 and it satisfies the requirement
But 876 also satisfies the requirement.
Insufficient
Statement 2: for c to be 2 after multiplication with 4, there are only 2 possibilities. C can be either 3 or 8
8 is not possible as a cannot be 10.
So the only possiblility is 543.
Sufficient
B
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If x is a three-digit number in which the hundreds digit is 1 greater 05 Apr 2020, 13:10
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CAMANISHPARMAR
If x is a three-digit number in which the hundreds digit is 1 greater than the tens digit and 2 greater than the units digit, then what is the value of x ?

1) When x is multiplied by 3, the tens digit of the result is 2.

2) When x is multiplied by 4, the units digit of the result is 2.
Show more

Let's start by translating the question statement into simpler language.

x is a 3-digit number, so it's something like 593 or 712.

The hundreds digit is "1 greater than the tens digit and 2 greater than the units digit." What numbers is this referring to? It's numbers where the hundreds digit is the greatest, then the next digit is 1 smaller, and the last digit is 1 smaller than that. In other words, our numbers must have 3 digits that are all decreasing by 1. The only possibilities are:

987
876
765
654
543
432
321
210

Since there are only a handful of possibilities, I'll probably actually jot these all down on my own paper, so I can look at them as I work through the statements.

We know that x must be one of these numbers. The question asks: which one?

1) When x is multiplied by 3, the tens digit of the result is 2.

Interesting. It would be easy to find the tens digit if I was multiplying the number by 10, for example. However, I don't know an easy way to find the tens digit after multiplying a number by 3. I'm going to start calculating based on my list above, and see if there's a pattern. I'll start with the smaller numbers, since those should be easier to multiply by 3.

210 * 3 = 630 - doesn't fit the statement, since the tens digit is 3
321 * 3 = 963 - doesn't fit the statement, since the tens digit is 6
432 * 3 = 1,296 - doesn't fit the statement, since the tens digit is 9

At this point, I realized that I don't need to do the whole calculation. Since I only want to know the tens digit, I only need to look at the tens digit and the units digit of each possible value of x. (However, this is starting to look like a time-consuming problem, and I may guess at this point if I'm behind on time.)

543*3 -> 43*3 = 129. This fits the statement! x might equal 543.

654*3 -> 54*3 = 162

765*3 -> 65*3 = 195

876*3 -> 76*3 = 228 This fits the statement! x might equal 876

We'll stop here, since we have two different possible values for x. We now know that this statement is insufficient.

2) When x is multiplied by 4, the units digit of the result is 2.

This statement will be much easier to work with, since we only need to look at the units digits, not the units AND tens digits like with the previous statement. We're only looking for values that have a units digit of 2 when multiplied by 4.

210*4 -> 0*4 -> 0
321*4 -> 1*4 -> 4
432*4 -> 2*4 -> 8
543*4 -> 3*4 -> 12 This fits the statement! x could be 543.
654*4 -> 4*4 -> 16
765*4 -> 5*4 -> 20
876*4 -> 6*4 -> 24
987*4 -> 7*4 -> 28

The only value of x that fits this statement, as well as the info in the question stem, is x = 543. Therefore, this statement is sufficient. The correct answer is B.
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If x is a three-digit number in which the hundreds digit is 1 greater 26 Feb 2022, 06:49
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