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GMAT Diagnostic Test Question 39

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GMAT Diagnostic Test Question 39 [#permalink]

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GMAT Diagnostic Test Question 39

Field: combinations
Difficulty: 650


Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252
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Last edited by Bunuel on 26 Nov 2013, 14:10, edited 5 times in total.
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Re: GMAT Diagnostic Test Question 39 [#permalink]

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New post 26 Nov 2013, 14:04
Could you update the question on this page to match the question in the downloadable PDF(8 small, 2 large). It took me a while to figure out that the solutions on this page don't match the question at the top of the page(7 small books, 3 large).
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Re: GMAT Diagnostic Test Question 39 [#permalink]

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New post 26 Nov 2013, 14:12
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UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D.
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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

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Re: GMAT Diagnostic Test Question 39 [#permalink]

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New post 16 Dec 2013, 04:24
Bunuel wrote:
UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D.



Dear Bunuel,
thanks a lot for your priceless help...
meanwhile could you give alternative way to solve with no formula? cause im just a beginner and it a bit hart to me to keep with formulas :( :oops:
thanks a lot :wink:
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Re: GMAT Diagnostic Test Question 39 [#permalink]

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New post 16 Dec 2013, 07:43
Expert's post
3111987 wrote:
Bunuel wrote:
UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D.



Dear Bunuel,
thanks a lot for your priceless help...
meanwhile could you give alternative way to solve with no formula? cause im just a beginner and it a bit hart to me to keep with formulas :( :oops:
thanks a lot :wink:


\(C^5_8=\frac{8!}{(8-5)!5!}=56\) is the number of ways we can choose 5 items out of 8.

Check below links for more:
Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html


Hope it helps.
_________________

New to the Math Forum?
Please read this: 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

Re: GMAT Diagnostic Test Question 39   [#permalink] 16 Dec 2013, 07:43
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