The average (arithmetic mean) of 4 different integers is 75. If the la

Question

The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?

A. 1
B. 19
C. 29
D. 30
E. 33

AmoyV · Accepted Answer

Total of Integers=75*4=300

Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.

But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89

Lowest of least possible integer = 300-(90+89+88)=300-267=33

Answer: E

gmatgrl · Answer

The average (arithmetic mean) of 4 different integers is 75.

This means that total of the 4 integers = 75*4 = 300
Largest is 90
This means that sum of the other 3 integers = 300 - 90 = 210

One can be 89, another 88 and so, the smallest one will be 210 - 89 - 88 = 33

OptimusPrepJanielle · Answer

Total of 4 integers = 75*4 = 300 Now largest integer is 90. So sum of remaining 3 different integers = 300-90 = 210. To get the lowest integer, the other 2 has to be as large as possible. So let us take 89 and 88 as the next 2 integers. So, lowest of least possible integer = 300-(90+89+88)=300-267=33 Hence option (E). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

Lucky2783 · Answer

if 90 is largest element the smallest will be 300 - 90 - 89- 88 =33

PareshGmat · Answer

Answer = E = 33

Let the other integers be 89 & 88

Setting up the equation to find the smallest integer "x"

\frac{90+89+88+x}{4} = 75

x = 300-267 = 33

tomlui2010 · Answer

Why can't it take 30 ?

assuming that the other three all have the max value = 90, which gives 90 *3 = 270

300 -270 = 30 ??

FightToSurvive · Answer

Please read the question properly, it clearly states, all the integers are different. ....

Hope it clears your doubt.

Posted from my mobile device

tomlui2010 · Answer

uh..oh!! my mistake :-D

lipsi18 · Answer

4 different integers, largest =90; AM=75
90+89+88+x=75*4; therefore x=300-90-89-88=33
Hence Answer is E

Thanks,

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: minimumvalue_text.PNG FAQ: Why can't the values be 90, 90, 90, and 30? The question states that we have four different integers, so we can only have one 90. The other numbers can't also be 90. FAQ: After a little calculation, we get a sum for 3 other integers equal to 210. Why can't the smallest integer be 1 for those 3 integers? The trick here is in noting that the largest integer is 90. So not only do the other three numbers have to total 210, but none of them can be larger than 90. If the smallest were 1, then the last two would have to add up to 209. This is impossible. FAQ: Why are the numbers in consecutive order: 88, 89, and 90? We are not choosing them because they are consecutive. This is the result of following the parameter set by the problem. No number is larger than 90. So, to find the least value of a number, we stack as much "weight" on the other numbers, and choose the next largest number possible after 90 (89). And since the numbers are all different, we have to again choose the next largest number (88). Thus 88 + 89 + 90.

stonecold · Answer

This is a great Question.
Here is my approach to this one =>

Let
w1
w2
w3
w4 => be the four integers in increasing order.

Using  Mean =\frac{Sum}{#}

Now Sum(4) = 75*4 = 300
w4=90

Now to minimise w1 we must maximise w1,w2
But since w3 is the largest integer => Both of them cannot be greater than 90
And remember the questions says that 4 integers are different
Hence the integers would be => 90,89,88

Hence w1=> 300-267=> 33
Hence E

NOTE=> If the word different is taken away from the original statement => Minimum value of w1 would've been 30.

Youraisemeup · Answer

Can someone solve it algebraically?

eman12771 · Answer

We know that the total of integers X, Y, W, and 90 = 4 * 75 = 300.
To find the minimum value of X, we want to maximize Y and W. Remember, the text says  different  integers, therefore, W = 90 - 1 = 89 & Y = 90 - 2 = 88. Now, we must find X -> X = 300 - 90 - 89 - 88 =  33 .

TarunKumar1234 · Answer

We have 90 +a+b+c = 75*4 = 300 or, a+b+c = 210 To make a smallest and b and c different, c = 89, b = 88. So, a = 210- (89+88) = 33. So, It is C.

bumpbot · Answer

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