Question: The sum of three numbers is 98. If the ratio between first and second be 2:3 and between second and third be 5:8, then the second number is:
(A) 30
(B) 20
(C) 48
(D) 58
(E) 60
“The sum of three numbers is 98. If the ratio between first and second be 2:3 and between second and third be 5:8”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Let the numbers be a, b, c
a+b+c = 98
a:b. b:c
2:3. 5:8
Now, we can find all the ratios common
a:b.
multiple this ratios by 5 (2:3) *5 =10:15
b:c
multiple this ratios by 3 (5:8) *3 = 15:24
Now new combined ratio: a:b:c
10:15:24
Now multiplying each ratio by a multiplier X, we can determine each value
Remember a+b+c =98
Therefore: 10x + 15x + 24x = 98
49x = 98
x = 2
Therefore the value of the second number, which is a = 15*2 = 30
Correct Answer: A
Approach Solution 2:
Given:
Sum Of 3 numbers= 98
Ratio of first number to second number is 2:3
Ratio of second number to third number is 5:8
Calculations:
Let the three numbers be A, B and C. Then,
A : B = 2:3 & B : C = 5:8
=5 X 3/5 : 8 X 3/5= 3 : 24/5
= A : B: C = 2 : 3 : 24/5
=10 : 15 : 24
= B = 98 X 15/49 = 30
Correct Answer: A
Approach Solution 3:
Let the three numbers be A,B and C respectively
A:B=2:3 (1)
B:C=5:8 (2)
Multiplying (1) by 5 and (2) by 3,
A : B=10:15
B : C=15:24
A : B : C=10 : 15 : 24
Sum of ratio = 10+15+24 = 49
B = 4915×90 = 30
Correct Answer: A
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