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Difficulty:
25%
(medium)
Question Stats:
73% (01:33) correct
27%
(01:58)
wrong
based on 89
sessions
History
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When a positive integer m is divided by 17, the remainder is 3. Which integer could be m?
I. 258
II. 274
III. 292
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
_________________
I. 258
II. 274
III. 292
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
_________________
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Bunuel
When a positive integer m is divided by 17, the remainder is 3.
In other words, m is 3 greater than some multiple of 17
Now let's find some multiples of 17 that are close to the given values...
(15)(17) = 255
(16)(17) = 272
(17)(17) = 289
Since 255 is a multiple of 17, we can see that 258 is 3 greater than some multiple of 17
So, m could equal 255.
So, we can eliminate answer choices B and C
Since 272 is a multiple of 17, we can see that 275 is 3 greater than some multiple of 17
So, m CANNOT equal 274
So, we can eliminate answer choice E
Since 289 is a multiple of 17, we can see that 292 is 3 greater than some multiple of 17
So, m could equal 292.
So, we can eliminate answer choice A
Answer: D
Let, m=20
When we devide m by 17 i.e., 20/17, we get 3 as remainder.
Hence,the options are divided by 17 with a remainder of 3, are our desired options.
Lets check out the options:
I. 258 (258/17) gives a remainder of 3
II.274 (274/17)gives a remainder of 2
III.292 (292/17) gives a remainder of 3
So, options I & III are the options that are devided by 17 with a remainder of 3.
Hence, D is our desired choice
Tusher Karmoker 🙂
Love from Bangladesh🇧🇩
Posted from my mobile device
When we devide m by 17 i.e., 20/17, we get 3 as remainder.
Hence,the options are divided by 17 with a remainder of 3, are our desired options.
Lets check out the options:
I. 258 (258/17) gives a remainder of 3
II.274 (274/17)gives a remainder of 2
III.292 (292/17) gives a remainder of 3
So, options I & III are the options that are devided by 17 with a remainder of 3.
Hence, D is our desired choice
Tusher Karmoker 🙂
Love from Bangladesh🇧🇩
Posted from my mobile device
Posts: 4,849
In a could be true question on GMAT we are trying to prove the statements true.
When, a positive integer m is divided by 17, the remainder is 3,we can infer that if we reduce the number (given as choices) by 3,the resulting numbers must be divisible by 17.
What are the numbers that we have when we reduce the given number by 3?
I. 258 - 3 =255
II. 274 - 3=271
III. 292 - 3 = 289
I occurs thrice, II twice and III thrice. It makes sense to start either with I or III to eliminate maximum choices.
I. 255 should be divisible by 17 - It is. Eliminate B,C.
III.289 we know is the square of 17. Divisible. Eliminate A
If you check II.271 iS NOT DIVISIBLE by 17 as 17 * 16 =272. Eliminate E.
(option d)
D.S
GMAT SME
When, a positive integer m is divided by 17, the remainder is 3,we can infer that if we reduce the number (given as choices) by 3,the resulting numbers must be divisible by 17.
What are the numbers that we have when we reduce the given number by 3?
I. 258 - 3 =255
II. 274 - 3=271
III. 292 - 3 = 289
I occurs thrice, II twice and III thrice. It makes sense to start either with I or III to eliminate maximum choices.
I. 255 should be divisible by 17 - It is. Eliminate B,C.
III.289 we know is the square of 17. Divisible. Eliminate A
If you check II.271 iS NOT DIVISIBLE by 17 as 17 * 16 =272. Eliminate E.
(option d)
D.S
GMAT SME
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The number should n]be of the form 17X+3
so when 3 is subtracted from the given numbers , the result should be a multiple of 17
among the options, (I) 258 and (III)292 satisfy this condition
so the answer is D
so when 3 is subtracted from the given numbers , the result should be a multiple of 17
among the options, (I) 258 and (III)292 satisfy this condition
so the answer is D
Correct Option D
Reminder formula : Dividend = Divisor * Quotient + Reminder
\(\frac{(Dividend - Reminder) }{ Divisor}\) = Positive integer (Quotient)
Option 1 = \(\frac{(258 - 3) }{ 17}\) = 15 - Correct
Optio. 2 = \(\frac{(274 - 3) }{ 17}\) = integer - Wrong
Option 3 = \(\frac{(292-3)}{17}\) = 17 - Correct
Correct Answer D (I and III)
Posted from my mobile device
Reminder formula : Dividend = Divisor * Quotient + Reminder
\(\frac{(Dividend - Reminder) }{ Divisor}\) = Positive integer (Quotient)
Option 1 = \(\frac{(258 - 3) }{ 17}\) = 15 - Correct
Optio. 2 = \(\frac{(274 - 3) }{ 17}\) = integer - Wrong
Option 3 = \(\frac{(292-3)}{17}\) = 17 - Correct
Correct Answer D (I and III)
Posted from my mobile device
When a positive integer m is divided by 17, the remainder is 3
Theory: Dividend = Divisor*Quotient + Remainder
m -> Dividend
17 -> Divisor
a -> Quotient (Assume)
3 -> Remainders
=> m = 17*a + 3 = 17a + 3
Which integer could be m
m = 17a + 3
=> m - 3 = 17a
=> m - 3 should be a multiple of 17.
We will take each option choice and subtract 3 and check if it is a multiple of 17 or not
I. 258
258 - 3 = 255 and we know that 255 IS a multiple of 17 => POSSIBLE
II. 274
274 - 3 = 271 and we know that 271 is NOT a multiple of 17 => NOT POSSIBLE
III. 292
292 - 3 = 289 and we know that 289 IS a multiple of 17 => POSSIBLE
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
_________________
Theory: Dividend = Divisor*Quotient + Remainder
m -> Dividend
17 -> Divisor
a -> Quotient (Assume)
3 -> Remainders
=> m = 17*a + 3 = 17a + 3
Which integer could be m
m = 17a + 3
=> m - 3 = 17a
=> m - 3 should be a multiple of 17.
We will take each option choice and subtract 3 and check if it is a multiple of 17 or not
I. 258
258 - 3 = 255 and we know that 255 IS a multiple of 17 => POSSIBLE
II. 274
274 - 3 = 271 and we know that 271 is NOT a multiple of 17 => NOT POSSIBLE
III. 292
292 - 3 = 289 and we know that 289 IS a multiple of 17 => POSSIBLE
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
_________________
How to Solve :
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
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