Brainteaser Answers – Issue 38, 2017

How’d you do? Now that you’ve had a chance to solve them it’s time to check your answers! We’re confident you got all or most of them correct. Whatever the case, we hope you enjoyed your mental break. Don’t fret we’ve already got next issues puzzles in the works and they’re sure to be as fun as these!

1.) Budget Fudget

On his first visit to the AutomationDirect website, a purchasing agent spent half his meager budget on a STRIDE industrial Ethernet switch, and then $5 on some cable ties*.  On his second visit, he spent half the remaining budget on a Photoelectric Sensor and $10 on a Cat5E Patch Cable.  On his third visit, he spent half the remaining budget on an Inductive Proximity Sensor, and $15 on a SureMotion Timing Pulley.  After the three purchases, he had $5 left in that particular budget.  What was the original budget amount?

*New SapiSelco cable ties now available in multiple colors and at even lower prices (as low as 1¢/tie, that’s right – just $1/100pk!) – www.go2ADC.com/sapiselco

Answer: 

He started with a budget of $210.

 

2.) DIY Quotes!

A customer called two automation suppliers for pricing on a pushbutton and a safety switch.  She was amazed when both distributors quoted the exact same prices for the two items over the phone.  She asked them to fax over formal quotes for both parts, but both distributors made mistakes at this point – one subtracted the cost of the push-button from the safety switch, and quoted $44.  The other multiplied the two prices and quoted $1280.  What were the original, verbally-quoted prices for the two items?

Did you know you can generate your own Formal 30-day Quotes right on the AutomationDirect website? Just click the Quotes button at the top of any webstore page OR visit   www.go2ADC.com/quotes

Answer:

The two quoted prices were $20 and $64.

We’re given that x=44+y and x*y=1280.  So substitute for x in the second equation and you will have y(y + 44) = 1280. Or written another way: y2 + 44y – 1280 = 0.  Use the quadratic equation to solve for y.  y = -128 or 20.  Rule out the negative price (nonsensical) and one of the items must have been quoted at $20.  The other would be $20 +44 = $64.

 

3.) Old Records/Pneu Records

Engineer Bob placed an order for a large quantity of pneumatic cylinders from AutomationDirect last year, but he promptly forgot what he bought, AND the unit price AND the quantity of the item he purchased.  He did remember that the total price for the parts was $47,867, excluding tax and shipping*.  His summer intern did some quick figuring, and a price check on the AutomationDirect.com website and announced that she knew exactly which item had been purchased, the quantity, and the price paid.  How did she do it?  Bonus: what was the price and quantity of the item?

*Remember that AutomationDirect.com offers free two-day shipping on all orders over $49 – and customers outside of Georgia don’t (currently) pay any sales tax.

** Also note that you can review all your past purchases online also – but that’s NOT how the intern solved this problem!

Answer:

47,867 is a somewhat special number; it is the product of two prime numbers: 151 and 317.  So, therefore the only four factors of 47,867 are: 1, 151, 317, and 47,867.  Since no pneumatics cylinders offered by AutomationDirect sell for $1 or for $47,867, the only two possibilities are that Bob purchased quantity 317 of a part costing $151, OR he purchased quantity 151 of a part costing $317.  Based on the currently posted price list (August 2017),  there are no pneumatics cylinders available that cost $151, however part number: D64020DT-MC with description “NITRA pneumatic air cylinder, NFPA tie rod, 4in bore, 2in stroke, double acting” is available for $317 as the intern was happy to inform her boss.  So he must have purchased quantity 151 of part number: D64020DT-MC at the price of $317.

Prices are subject to change at any time.  If you deduced that the two numbers were 151 and 317 (regardless of which was the price and which was the quantity) then congratulations, you solved this riddle!