This set of Aptitude Questions and Answers (MCQs) focuses on “Fractions”.
1. Find the reduced form of \(\frac{174}{377}\).
a) 6/13
b) 5/17
c) 7/19
d) 11/21
View Answer
Explanation: 174 = 29*6 and 377 = 29*13.
HCF is 29.
On dividing both numerator and denominator of \(\frac{174}{377}\) by 29, we get, \(\frac{6}{13}\).
2. Find the largest number among \(\frac{5}{6}, \frac{3}{7}, \frac{7}{18}, \frac{11}{21} and \frac{13}{30}\).
a) 13/30
b) 3/7
c) 11/21
d) 5/6
View Answer
Explanation: To find the largest or smallest number, we must have a common denominator.
LCM of denominators ie., 6, 7, 18, 28 and 30 is 630.
\(\frac{5}{6}=\frac{5*630}{6*630}=\frac{525}{630}, \frac{3}{7}=\frac{3*630}{7*630}=\frac{270}{630}, \frac{7}{18}=\frac{7*630}{18*630} = \frac{245}{630}, \frac{11}{21}=\frac{11*630}{21*630}=\frac{330}{630} and \frac{13}{30}=\frac{13*630}{30*630}=\frac{273}{630}\).
Therefore, the largest number is \(\frac{525}{630}=\frac{5}{6}\).
3. Find the LCM of \(\frac{5}{9}, \frac{6}{7}, \frac{9}{13} and \frac{11}{15}\).
a) 990/7
b) 330/7
c) 990
d) 330
View Answer
Explanation: LCM of fractions = \(\frac{LCM \, of \, numerators}{HCF \, of \, denominators}\).
LCM of \(\frac{5}{9}, \frac{6}{7}, \frac{9}{13} and \frac{11}{15} = \frac{LCM \, of \, 5,6,9 \, and \, 11}{HCF \, of \, 9,7,13 \, and \, 15}=\frac{990}{1}\)=990.
4. Find the HCF of \(\frac{65}{3},\frac{91}{12},\frac{143}{20} and \frac{195}{26}\).
a) 13/780
b) 17/780
c) 19/840
d) 11/840
View Answer
Explanation: HCF of fractions = \(\frac{LCM \, of \, numerators}{HCF \, of \, denominators}\).
HCF of \(\frac{65}{3},\frac{91}{12},\frac{143}{20} and \frac{195}{26}=\frac{HCF \, of \, 65,91,143 \, and \, 195}{LCM \, of \, 3,12,20 \, and \, 26}=\frac{13}{780}\).
5. If X, Y and Z are three numbers, such that LCM of X and Y is X and LCM of Y and Z is Y, then find the HCF of X, Y and Z.
a) X
b) Y
c) Z
d) XY
View Answer
Explanation: Let X=168, Y=84 and Z=21, such that LCM of 168 and 84 is 168 and LCM of 84 and 21 is 84, such that it satisfies all the given conditions.
Therefore, HCF of 168, 84 and 21 is 21 i.e., Z.
6. If P, Q and R are three numbers, such that HCF of P and Q is P and HCF of P and R is R, then find the LCM of P, Q and R.
a) PR
b) QR
c) R
d) Q
View Answer
Explanation: Let P=48, Q=96 and R=12, such that HCF of 48 and 96 is 48 and HCF of 48 and 12 is 12, such that it satisfies all the given conditions.
Therefore, LCM of 48, 96 and 12 is 96 i.e., Q.
7. If x and y are two distinct positive integers, then find the HCF of \(\Big(\frac{x}{HCF(x,y)},\frac{y}{HCF(x,y)}\Big)\).
a) y
b) x
c) 1
d) x/y
View Answer
Explanation: For any positive integral values of x and y, the HCF of \(\Big(\frac{x}{HCF(x,y)},\frac{y}{HCF(x,y)}\Big)\) is 1.
For example, take x=21 and y=7, such that HCF of 21 and 7 is 7.
Therefore, HCF of \(\Big(\frac{x}{HCF(x,y)},\frac{y}{HCF(x,y)}\Big)\)=HCF of \(\Big(\frac{21}{7},\frac{7}{7}\Big)\)=HCF of 3,1 is 1.
8. For integers x, y and z, LCM(x,y) is x and LCM(y,z) is y, then find the LCM(x,y,z).
a) z
b) x
c) y
d) xyz
View Answer
Explanation: Let x=75, y=25 and z=5, such that LCM(x,y) is x=75 and LCM(y,z) is y=25.
Now, the LCM of x, y and z is 75 i.e., x.
9. If HCF and LCM of two fractions is 5/54 and 10/9 and if one of the fractions is 10/27, find the other.
a) 5/18
b) 10/18
c) 5/27
d) 10/9
View Answer
Explanation: We know that product of numbers = HCF*LCM.
Other fraction = \(\frac{\frac{5}{54}*\frac{10}{9}}{\frac{10}{27}}=\frac{5}{18}\).
10. If HCF of two fractions is 20 times the LCM and the product of two fractions is 125/324, the find the HCF.
a) 5/18
b) 5/36
c) 15/36
d) 15/18
View Answer
Explanation: We know that product of numbers = HCF*LCM.
Let HCF be x, so that LCM is 20x.
x * 20x = 125/324.
Therefore, HCF = x = 5/36.
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