The given question is a challenging GMAT 700+ level quant problem solving question combining concepts in linear equations and elementary number properties.

Question 19: Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?

- 5
- 2
- 9
- 3
- 7

@ INR

Total dollar value of all gift certificates in the initial configuration : 13 hampers × 12 dollars = $156

Total dollar value of all gift certificates in the new configuration = 12 hampers × 13 dollars = $156

No change in total value of gift certificates.

Susan started with 13 hampers.

So, she has 13 of $3, 13 of $4, and 13 of $5 certificates.

In the new configuration, $13 can be achieved as follows: {3, 3, 3, 4}, {4, 4, 5}, and {5, 5, 3}

The hampers that contain the configuration {3, 3, 3, 4} will not have $5 certificates.

Let Susan make x hampers of {3, 3, 3, 4}, y hampers of {4, 4, 5}, and z hampers of {5, 5, 3}.

The answer to ‘x’ is the answer to the question.

Number of $3 certificates will be 3x + z = 13 ....(1)

Number of $4 certificates will be x + 2y = 13 ....(2)

Number of $5 certificates will be y + 2z = 13 ....(3)

**Multiply (3) by 2**: 2y + 4z = 26

__Subtract (2) from (3) × 2__

2y + 4z = 26

-x - 2y = -13

------------------

4z – x = 13 ....(4)

------------------

**Multiply (1) by 4**: 12x + 4z = 52

__Subtract (4) and (1) × 4__

12x + 4z = 52

-4z + x = -13

----------------

13x = 39

-----------------

Or x = 3

'x' is the number of gift hampers without $5 certificates.

As x = 3, three gift hampers did not contain $5 gift certificates.

Try it free!

Register in 2 easy steps and

Start learning in 5 minutes!

11. GMAT 700 Level Sample Question in Statistics

12. GMAT Hard Math Algebra - Absolute Values | GMAT Problem Solving

13. GMAT Challenging Question | Statistics Problem Solving

14. GMAT Hard Math | Arithmetic | Permutation Combination Sample Question

15. GMAT Challenging Math Question | Arithmetic | Number Properties DS Practice

16. 700 800 Level GMAT Word Problem | Number Properties & Equations Problem Solving Question

17. GMAT DS Sample Question | Geometry | Triangles

18. GMAT 700 800 Level Question | Coordinate Geometry & Permutation Combination

19. GMAT Hard Math Question | Algebra | Difficult Equations Question

20. GMAT Hard Math Questions | Arithmetic | Number Properties DS

Copyrights © 2016 - 21 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

48/1 Ramagiri Nagar

Velachery Taramani Link Road.,

Velachery, Chennai 600 042. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message