In a computer repair shop the ratio of the number of CPUs to

Question

In a computer repair shop the ratio of the number of CPUs to the number of motherboards to the number of keyboards to the number of mouse pads is 2:3:5:7. What is the difference in the total number of keyboards and mother boards?

(1) The number of keyboards lies between 6 to 14.
(2) The difference between the total number of mouse pads and CPUs is 10.

alnewton · Answer

According to the given ratio,

CPU:MB:KB:Mo = 2:3:5:7

Assuming no. of CPU's -> 2x
 MB -> 3x 
 KB -> 5x
 Mo -> 7x

1) KB lies between 6 and 14
No of KB = 5x, The only ,multiple of 5 between 6 to 14 is 10
Thus no. of KB's = 10,  x=2 .  Suff. 
2) Mo - CPU = 7x - 2x =10
 5x = 10 =>  x=2 .  Suff. 
Ans. D. Each statement ALONE is sufficent

Bunuel · Answer

In a computer repair shop the ratio of the number of CPUs to the number of motherboards to the number of keyboards to the number of mouse pads is 2:3:5:7. What is the difference in the total number of keyboards and mother boards?

Given: {CPU}:{Motherboards}:{Keyboards}:{Pads}=2x:3x:5x:7x, for some positive integer multiple x.

(1) The number of keyboards lies between 6 to 14 --> 6<5x<14 --> {Keyboards}=5x=10 --> x=2 --> {Motherboards}=3x=6 --> {Keyboards}-{Motherboards}=10-6=4. Sufficient.

(2) The difference between the total number of mouse pads and CPUs is 10 --> {Pads}-{CPU}=7x-2x=10 --> 5x=10 -->x=2. The same info as above. Sufficient.

Answer: D.

KrishnakumarKA1 · Answer

PROMPT ANALYSIS
Let total number of device be T
CPU = 2T/17
Motherboard = 3T/17
Keyboards = 5T/17
Mouse pad = 7T/17

SUPERSET
T will a natural number multiple of 17.

TRANSLATION
In order to find T:
1# we need exact value of T
2# another equation with T as variable.

Statement Analysis

St 1: Since T/17 will yeild an integer, 5T/17 will also be an integer.Between 6 and 14, only 10 is a mutiple of 5. Hence no. of keyboards =10. No. of motherboards = 6 and T =38. Therfore the difference is 4.ANSWER. Option b,c and e eliminated.

St 2: 7T/17 -2T/17 = 10 or 5T/17 = 10 or T=38. Hence no. of keyboards =10. No. of motherboards = 6. Therfore the difference is 4.ANSWER. Option a eliminated.

Option D

pingala · Answer

The thing with ratio's i keep stumbling on is that, for example, a ratio 2:3 is not simply a number but a relationship that has an unspecified shared variable.

This isn't apparent to me when I approach these problems, simply running into them to solve and move on. Thats why I keep tripping up on fairly simple Quant questions like this.

So in 2:3 its actually 2x:3x, where x is that shared unspecified variable. It helps me to think of that when I see a ratio problem. All the comments specified that in their explanations, but I wanted to make sure I spell it out as a reminder to myself that I trip on this aspect.

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