Question: When the numbers 5, 7, 11 divide a positive multiple of 17, the remainders left are respectively 4, 6, and 10. Which positive multiple of 17 gives the least number that satisfies the given condition?
- 315th
- 316th
- 317th
- 384th
- 385th
Solution and Explanation
Approach Solution (1):
We can see that the difference between the divisor and remainder is constant = 1
5 – 4 = 1
7 – 6 = 1
11 – 10 = 1
So the least number will be 1 less than the LCM (5, 7, 11)
LCM (5, 7, 11) = 385, Least such number = 385 – 1 = 384
Since the number has to be a multiple of 17, it will be of the form 385n – 1 = 17k
The least such number is 5389 = 17 * 317
Correct option: C
Approach Solution (2):
In this question, we will use the Units Digit Analysis Method.
We will start with the first three answer choices.
1st positive multiple of 17 = 1 * 17 = 17
2nd positive multiple of 17 = 2 * 17 = 34
And so on
We are looking for the least positive multiple of 17
Given: 17m = 385k – 1
This can be written as: 385k = 17m + 1
On the LHS of the equation, the factor 385 multiplied by any non-negative integer k will yield a Units Digit of either 0 or 5.
Therefore, the RHS must yield a Units Digit of 0 and 5
This can also be read as: 17m + 1 must yield a Units Digit of 0 and 5
(1) 315th positive multiple of 17
(17) (315) + 1 (units digit of 6)
(2) 316th positive multiple of 17
(17) (316) + 1 (units digit of 3)
(3) 317th positive multiple of 17
(17) (317) + 1 (units digit of 0)
(4) 384th positive multiple of 17
(17) (384) + 1 (units digit of 9)
(5) 385th positive multiple of 17
(17) (385) + 1 (units digit of 6)
The only possible answer that could work is (c) 317th positive multiple of 17 = 5, 389
Correct option: C
Approach Solution (3):
Given:\(\frac{(17*Unkown)}{5}\)
Remainder: 4
Multiply each no's last digit by 7 if 17, we will get:
A. 315th: 7*5 = 35 =\(\frac{35}{5}
\)(Perfectly divide, no remainder)
B. 316th: 7*6 = 42 =\(\frac{30}{5}\)(Perfectly divide, remainder= 2)
C. 317th: 7*7 = 49 =\(\frac{49}{5}\)(Perfectly divide, remainder= 4)
D. 384th: 7*4 = 28 =\(\frac{28}{5}\)(Perfectly divide, remainder= 3)
E. 385th: 7*5 = 35 =\(\frac{35}{5}\)(Perfectly divide, no remainder)
Correct option: C
“When the numbers 5, 7, 11 divide a positive multiple of 17, the remainders left are respectively 4, 6, and 10. Which positive multiple of 17 gives the least number that satisfies the given condition?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Suggested GMAT Problem Solving Questions:
- A password to a certain database consists of digits that can GMAT Problem Solving
- A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
- The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
- Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
- For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
- The quantities S and T are positive and are related by the equation GMAT Problem Solving
- A child paints the six faces of a cube with six different GMAT Problem Solving
- In an opera theater. there are 300 seats available GMAT Problem Solving
- At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
- NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
- Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
- A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
- If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving
- What Is The Units Digit Of The Product Of Any Five Consecutive Positive Integers GMAT Problem Solving
- A Large Cube Consists Of 125 Identical Small Cubes GMAT Problem Solving
- A Pizzeria Makes Pizzas That Are Shaped As Perfect Circles GMAT Problem Solving
- The Number Of Diagonals Of A Polygon Of n Sides Is Given By The Formula GMAT Problem Solving
- The Work Done By A Woman In 8 Hours Is Equal To The Work Done By A Man GMAT Problem Solving
- A Circle Is Inscribed Inside Right Triangle Abc Shown Above GMAT Problem Solving
- The Temperatures In Degrees Celsius Recorded At 6 In The Morning In GMAT Problem Solving
- A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
- If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
- The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
- A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
- The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
- When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
- When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
- Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving
- If the mean of set S does not exceed mean of the subset of set S, which GMAT Problem Solving
- A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving
- It Was Observed by National Geographic that Equinox Happened GMAT Problem Solving
- Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving
- What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving
- In A Locality, There Are Ten Houses In A Row. On A Particular Night GMAT Problem Solving
- The “Connection” Between Any Two Positive Integers a And b GMAT Problem Solving
- Find the least positive integers which must be added to 15,463 so that the result GMAT Problem Solving
- Mayank Buys Some Candies for $15 a dozen and An Equal Number of Different GMAT Problem Solving
- If John Throws a Coin Until a Series of Three Consecutive Heads GMAT Problem Solving
- In the Diagram Above, ABCD is a Parallelogram and the Areas of Yellow GMAT Problem Solving
- On certain road 10% of the motorists exceed the posted speed limit GMAT Problem Solving
- If n is a positive integer and the product of all the integers from 1 to n GMAT Problem Solving
- John has 10 pairs of matched socks. If he loses 7 individual socks GMAT Problem Solving
- If x is an integer and 4^x < 100, what is x? GMAT Problem Solving
- The ratio 2 to 1/3 is equal to the ratio GMAT Problem Solving
- In the Decimal Notation of Number (2/23)^3. What is the Third Digit GMAT Problem Solving
- Tom Read a Book Containing 480 Pages by Reading the Same Number GMAT Problem Solving
- A 100-litre Mixture of Milk and Water Contains 36 litres of Milk GMAT Problem Solving
- The Figure shows the Graph of y = (x + 1)(x - 1)^2 in the xy-plane GMAT Problem Solving
- On the Graph above, When x = 1/2, y = 2; and when x = 1, y = 1 GMAT Problem Solving
- A Box Contains 100 Balls, Numbered From 1 To 100 GMAT Problem Solving