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M70-02

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M70-02  [#permalink]

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New post 03 Sep 2018, 01:56
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A
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C
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If x is a positive integer that is less than 20, what is x?

(1) \(x + 7\) divided by 5 has a remainder of 1.

(2) \(x\) divided by 4 has a remainder of 2.

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Re M70-02  [#permalink]

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New post 03 Sep 2018, 01:56
Official Solution:


We’ll go for PRECISE because all the information we need is in the question.

(1) If \(x\) is a positive integer under 20, \(x + 7\) must be a positive integer under 27. The integers in this range that have a remainder of 1 when divided by 5 are those that are larger by 1 than a multiple of 5: these are the numbers 1, 6, 11, 16, 21, and 26 – meaning that x can be 4, 9, 14 or 19. But which one? (A) and (D) are eliminated.

(2) The numbers under 20 that have a remainder of 2 when divided by 4 are larger by 2 than a multiple of 4: 2, 6, 10, 14, and 18, so we don’t have a definite result. (B) is eliminated. Combining (1) and (2) leaves only 14 as a possible answer. Enough! (E) is eliminated.


Answer: C
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New to the Math Forum?
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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.


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Re M70-02 &nbs [#permalink] 03 Sep 2018, 01:56
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