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Mental mathematics - under various guises - is a skill of rapid calculations; arithmetic calculations being the most common variety. Those who possess an innate aptitude for mental mathematics are k

According to USFDA, a combination product is one composed of any combination of a drug and device; biological product and device; drug and biological product

nown as human calculators. They may not even know why their methods work, but with a few rare exceptions, those methods have a simple algebraic explanation. Practice and understanding of th

; or drug, device, and biological product and fixed dose combination would include two or more combinations of drug.

Examples of combination products may in

e basics help the regular folks who were not born the human calculators acquire the necessary skill. But is the skill of mental calculations indeed necessary? Candidly? Nothing is. However, masterin

lude drug-coated devices, drugs packaged with delivery devices in medical kits, and drugs and devices packaged separately but intended to be used together.

g a skill may prove an invaluable asset.

Mental mathematics has many uses that mainly fall into three categories which I call defensive, offensive, and entertaining. The

here is enormous increase in the number of combination products entering the market in the recent years. Combination products have proven advantages but fixe

distinction between the three categories may at times be fuzzy, but in essence you may need to compute fast in order to verify a result obtained somehow else and to avoid a mistake, or to get a resu

d dose combinations are still in the process of convincing regulatory authority on their advantages over the single ingredient formulations.

Combination pro

lt fast in the first place, or just to show off and stun and please friends with your mastery of mysterious tricks.

In the way of example, without actually computing say 127?18 select the product f

ucts have become life saving products for the pharmaceutical companies who doesn’t have many innovative molecules in their product pipeline and have been inc

rom the list of numbers below:

2284,
22886,
2286,
2886.

Well, note that 18 is divisible by 9 (and 3) so is the product 127?18. The number is divisible b

easingly used in the product life cycle management. Even the companies having product patents are trying to extend their product life cycle through the combi

y 3 if the sum of its digits is divisible by 3. This disqualifies the first number 2284 as the sum of its digits is 16 and is not divisible by 3. (Also, the last digit of the product is defined by t

nation products and maximize the revenues. But the companies involved in this practice are overlooking that they are burdening the patients both economically

he last digits if the multiplicands, which in this case are 7 and 8. So that last digit of the product is bound to be 6.) The second number 22886 is way too big. To see that, replace 127 and 18 with

and physically. They need to rightly judge the benefits of the combination products and they have to even look at the risks involved when combining the produ

bigger numbers, e.g. 200 and 20. Easily, 200?20 = 4000 which is bigger than the product 127?18 but far off the oversized candidate 22886. The third number 2286 does not fail in an obvious way, but

ts. Some of the combination products were well accepted by physicians while others suffered. Companies involved in development of combination products are fi

the fourth one, 2886, does. Similarly, to the second possible answer, this one is also too big, but not as much. If we replace 127 with 130 and 18 with 20, the product will grow. But 130?20 is 2600

ding difficulty in defining their combination products and facing various challenges from selecting a combination to marketing it.

Following aspects would a

still less than 2886 and so is the sought product. Thus the third number is the only plausible choice. Can you compute fast 95?96? Why, there are many ways to do that. For example,

95?96= 95?95 + 9

dd to the challenges in developing combination products:

Which markets to tap where the combination products can do fairly well?
Which combination prod

5 = 9025 + 95 = 9120. The first step is an application of the distributive law, the second an application of a rule for the square of numbers ending in 5. To compute 95?95, first drop five

cts are meaningful and rational?
Which therapeutic categories to select?
Which Combinations can address unmet needs of the patients?
Do combin

to obtain 9. Multiply the latter by one more than the number itself: 9?10 = 90. Next, append 25.

As another example, what is 97?103? Quickly,

97?103= 100·100 - 3·3 = 10000 - 9 = 9991

tions increase the patient compliance?
What would be the developing cost?
How to tackle the risks encountered during combination product developmen

. Why? Because of the general formula (a - b)·(a + b) = a·a - b·b, which comes in handy if we observe that 97 = 100 - 3 and 103 = 100 + 3.

One of the simplest entertaining tricks is this. Take a th

t?

As combination products don't fit into the traditional categories of drugs, medical devices, or biological products, the USFDA is in the process of devel

ree digits number and subtract from it the sum of its digits. (You may need to sum up the digits one more time until you get a 1-digit number.) Tell me any two digits of the result. I'll respond wit

ping new procedures for reviewing their safety, efficacy and quality.

Professional from academic institutions, pharmaceutical industries, health care indust

h the remaining digit. For example, assume you chose number 573 whose digits ad up to 15. This is a two digit number. So we replace it with the sum of the digits, which is 6. Subtract now 6 from 573

y and representatives from various regulatory agencies are working out to design the regulatory requirements for manufacture and sale of combination products

. 573 - 6 = 567. Note that the three digits of the result (5, 6, 7) add up to 18, a multiple of 9. This is always the case. Now, if you announce the first two digits of the result, 5 and 6, I comput

.

As there is an increasing trend of the combination products companies manufacturing such products should be able to tackle the problems involved in the de

e their sum, which is 11, and find the first multiple of 9 exceeding that number. The first multiple of 9 greater than 11 is 18. Now the difference 18 - 11 = 7 gives me the last digit of your result

elopment. They need to be wiser in analyzing the market trends and the regulatory requirements.

Companies that provide selfless information through particip

.

Try this trick with your friends. And if you like to learn more, have a look at my page Fast Arithmetic Tips

tion in industry events and feedback to regulatory authorities would be able to face the challenges and will be successful in developing combination products

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