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The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If (2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?
- a)21
- b)200
- c)210
- d)300
- e)310
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The three-digit positive integer x has the hundreds, tens, and units d...
First, let us simplify the exponential equation:
When the bases on both sides of an equation are equal and the bases are prime numbers, the exponents of the respective bases must also be equal: a = k + 2; b = l + 1; and c = m . Now recall that a , b , and c represent the hundreds, tens, and units digits of the three-digit integer x ; similarly, k , l , and m represent the hundreds, tens, and units digits of the three-digit integer y .
Therefore, the hundreds digit of x is 2 greater than the hundreds digit of y ; the tens digit of x is 1 greater than the tens digit of y ; finally, the units digit of x is equal to the units digit of y . Using this information, we can set up our subtraction problem and find the value of (x – y ):
When the bases on both sides of an equation are equal and the bases are prime numbers, the exponents of the respective bases must also be equal: a = k + 2; b = l + 1; and c = m . Now recall that a , b , and c represent the hundreds, tens, and units digits of the three-digit integer x ; similarly, k , l , and m represent the hundreds, tens, and units digits of the three-digit integer y .
Therefore, the hundreds digit of x is 2 greater than the hundreds digit of y ; the tens digit of x is 1 greater than the tens digit of y ; finally, the units digit of x is equal to the units digit of y . Using this information, we can set up our subtraction problem and find the value of (x – y ):
Most Upvoted Answer
The three-digit positive integer x has the hundreds, tens, and units d...
We have that $12(2k)(3l)(5m) = (2a)(3b)(5c)$. Dividing both sides by $12$, we have $(2k)(3l)(5m) = (a)(b)(c)$. Since $x$ and $y$ are three-digit positive integers, we have $100 \leq x,y \leq 999$, so $1 \leq a,b,c,k,l,m \leq 9$, which means that $2k$, $3l$, and $5m$ are all factors of $(a)(b)(c)$.
Since $2k$ is a factor of $(a)(b)(c)$, we know that $k$ is a factor of $(a)(b)(c)/2$. Since $a$, $b$, and $c$ are single-digit positive integers, we know that $(a)(b)(c)/2$ is a multiple of $1/2 = 1$, $2$, $3$, $4$, or $6$. Therefore, $k$ is a factor of $1$, $2$, $3$, $4$, or $6$. Since $k$ is a single-digit positive integer, we must have $k = 1$, $k = 2$, $k = 3$, $k = 4$, or $k = 6$.
If $k = 1$, then $(2k)(3l)(5m) = 30lm$, and $(a)(b)(c) = 30lm$. Since $1 \leq l,m \leq 9$, we know that $30lm$ is a multiple of $30$, but it is not divisible by $100$, so $x \neq 30lm$.
If $k = 2$, then $(2k)(3l)(5m) = 60lm$, and $(a)(b)(c) = 60lm$. Since $1 \leq l,m \leq 9$, we know that $60lm$ is a multiple of $60$, but it is not divisible by $100$, so $x \neq 60lm$.
If $k = 3$, then $(2k)(3l)(5m) = 180lm$, and $(a)(b)(c) = 180lm$. Since $1 \leq l,m \leq 9$, we know that $180lm$ is a multiple of $180$, but it is not divisible by $100$, so $x \neq 180lm$.
If $k = 4$, then $(2k)(3l)(5m) = 120lm$, and $(a)(b)(c) = 120lm$. Since $1 \leq l,m \leq 9$, we know that $120lm$ is a multiple of $120$, but it is not divisible by $100$, so $x \neq 120lm$.
If $k = 6$, then $(2k)(3l)(5m) = 180lm$, and $(a)(b)(c) = 180lm$. Since $1 \leq l,m \leq 9$, we know that $180lm$ is a multiple of $
Since $2k$ is a factor of $(a)(b)(c)$, we know that $k$ is a factor of $(a)(b)(c)/2$. Since $a$, $b$, and $c$ are single-digit positive integers, we know that $(a)(b)(c)/2$ is a multiple of $1/2 = 1$, $2$, $3$, $4$, or $6$. Therefore, $k$ is a factor of $1$, $2$, $3$, $4$, or $6$. Since $k$ is a single-digit positive integer, we must have $k = 1$, $k = 2$, $k = 3$, $k = 4$, or $k = 6$.
If $k = 1$, then $(2k)(3l)(5m) = 30lm$, and $(a)(b)(c) = 30lm$. Since $1 \leq l,m \leq 9$, we know that $30lm$ is a multiple of $30$, but it is not divisible by $100$, so $x \neq 30lm$.
If $k = 2$, then $(2k)(3l)(5m) = 60lm$, and $(a)(b)(c) = 60lm$. Since $1 \leq l,m \leq 9$, we know that $60lm$ is a multiple of $60$, but it is not divisible by $100$, so $x \neq 60lm$.
If $k = 3$, then $(2k)(3l)(5m) = 180lm$, and $(a)(b)(c) = 180lm$. Since $1 \leq l,m \leq 9$, we know that $180lm$ is a multiple of $180$, but it is not divisible by $100$, so $x \neq 180lm$.
If $k = 4$, then $(2k)(3l)(5m) = 120lm$, and $(a)(b)(c) = 120lm$. Since $1 \leq l,m \leq 9$, we know that $120lm$ is a multiple of $120$, but it is not divisible by $100$, so $x \neq 120lm$.
If $k = 6$, then $(2k)(3l)(5m) = 180lm$, and $(a)(b)(c) = 180lm$. Since $1 \leq l,m \leq 9$, we know that $180lm$ is a multiple of $
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The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer?
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The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer?.
The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer?.
Solutions for The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. Thethree-digit positive integer y has the hundreds, tens, and units digits of k, l , and m, respectively. If(2a)(3b)(5c) = 12(2k)(3l)(5m), what is the value of x – y?a)21b)200c)210d)300e)310Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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