Official Solution:The product of a positive integer \(x\) and 377,910 is divisible by 3,300, then the least value of \(x\) is:

A. \(10\)

B. \(11\)

C. \(55\)

D. \(110\)

E. \(330\)

Given: \(\frac{377,910*x}{3,300}=integer\).

Factorize the divisor: \(3,300=2^2*3*5^2*11\).

Check 377,910 for divisibility by \(2^2\): 377,910 IS divisible by 2 and NOT divisible by \(2^2=4\) (since its last two digits, 10, is not divisible by 4). Thus \(x\) must have 2 as its factor (377,910 is divisible only by 2 so in order \(377,910*x\) to be divisible by \(2^2\), \(x\) must have 2 as its factor);

Check 377,910 for divisibility by 3: 3+7+7+9+1+0=27, thus 377,910 IS divisible by 3.

Check 377,910 for divisibility by \(5^2\): 377,910 IS divisible by 5 and NOT divisible by 25 (in order a number to be divisible by 25 its last two digits must be 00, 25, 50, or 75, so 377,910 is NOT divisible by 25). Thus \(x\) must have 5 as its factor.

Check 377,910 for divisibility by 11: \((7+9+0)-(3+7+1)=5\), so 377,910 is NOT divisible by 11, thus \(x\) must have 11 as its factor.

Therefore the least value of \(x\) is \(2*5*11=110\).

Answer: D

_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics